- 18.440 Problem Set 10 Due in class Friday December 5; late work will not be accepted. You can discuss
- Representations of Lie Groups 18.758 The goal of this course is to explain some of the ideas in the "local Langlands conjectures." Since the
- 18.781 Exam 1 solutions Friday, October 7, 2005
- CURRICULUM VITAE David A. Vogan, Jr.
- KL polys for Adams et al.
- BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY
- Unitary Representations and Complex Analysis David A. Vogan, Jr ?
- CURRICULUM VITAE David A. Vogan, Jr.
- 2. HARMONIC ANALYSIS ON COMPACT GROUPS. These notes recall some general facts about Fourier analysis on a compact gr*
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- noblackboxes The Orbit Method and Unitary Representations for Reduc* *tive Lie Groups |
- Calculating Adams et al.
- THREEDIMENSIONAL SUBGROUPS AND UNITARY REPRESENTATIONS
- UNITARY SHIMURA CORRESPONDENCES FOR SPLIT REAL GROUPS
- April 15, 2011 18.01 Problem Set 11
- Calculating Adams et al.
- 18.440 Problem Set 7 Due in class Monday October 27; late work will not be accepted. You can discuss
- 18.440 Problem Set 5 Due in class Monday October 6; late work will not be accepted. You can discuss
- 18.700 Problem Set 2 Solutions Unless otherwise noted, the eld of scalars is the real numbers.
- 18.02A PROBLEM SET 13 Due in recitation Tuesday, March 16
- 18.02A PROBLEM SET 11 Due in recitation Tuesday, February 24
- Calculating Adams et al.
- 18.104, Solutions to fth problem set Problem 1 (page 294, #4). This asked you to show that
- 18.02A PROBLEM SET 10 SOLUTIONS 1. (10 points) A function f(x, y) of two variables is called harmonic if
- 18.02A PROBLEM SET 9 SOLUTIONS 1. (10 points) The Lasker Rink in the northeast corner of Central Park is a perfect
- Notes on Picard's method In class on Friday I was sloppy about a number of things; so here is a slightly more
- Isolated unitary representations. David A. Vogan, Jr. *
- 18.440 Problem Set 2 Due in class Monday September 15; late work will not be accepted. You can
- 18.02A Second Half, Spring Semester 2004 General Information
- 18.700 Problem Set 4 solutions 1. (15 points) Suppose that p and q are positive integers with p+q = n.
- Geometric quantization for nilpotent coadjoint orbits William Graham *
- Here are some practice problems you might use in preparing for the nal exam. I'm sorry to say that I won't have a chance to post solutions to these problems
- 18.781 Problem Set 3 Due Monday, September 26 in class. In each of these problems, the last part is
- SOLUTIONS TO HOMEWORK 6 1. Suppose that
- CORRECTIONS FOR LECTURES ON THE ORBIT METHOD, BY A.A. KIRILLOV.
- The translation David Vogan
- SOLUTIONS TO HOMEWORK 3 Due Monday, September 26 in class. In each of these problems, the last part is
- 18.02A PROBLEM SET 10 SOLUTIONS 1. (10 points) A function f(x, y) of two variables is called harmonic if
- 18.700 Problem Set 3 solutions 1. (10 points) Suppose a, b, c, and d are elements of a eld F. Use
- Representations of Lie Groups 18.757 This will be an introduction to representation theory, intended for tourists as well as for
- 18.02A PROBLEM SET 13 SOLUTIONS 1. (10 points) This problem concerns an analogue of the theory of conservative fields
- Representations of Lie Groups 18.758 The goal of this course is the classification of the (possibly infinitedimensional) irreducible
- UNITARY SHIMURA CORRESPONDENCES FOR SPLIT REAL GROUPS
- 18.440 Problem Set 2 Due in class Monday September 15; late work will not be accepted. You can
- The Langlands Classification and Irreducible Characters for Real Reductive Groups
- 18.440 Probability and Random Variables Fall Semester, 2003 Supplementary notes on continuous random variables
- 18.700 nal review problems I'll try to post some solutions Saturday 12/14.
- Representations of Lie Groups 18.758 This will be an introduction to the in nite-dimensional unitary representations of reductive Lie
- 18.034 Problem Set 6 Due Monday, April 10 in class.
- The character table for E8 David Vogan*
- 00 0000 0000 THE LOCAL LANGLANDS CONJECTURE David A. Vogan, Jr.
- 18.700 Problem Set 3 Due in class Monday October 23; late work will not be accepted. Your work on
- Isolated unitary representations. David A. Vogan, Jr. *
- SOLUTIONS TO HOMEWORK 4 Due Monday, October 3 in class.
- 18.02A PROBLEM SET 12 SOLUTIONS 1. (10 points) This problem is about the unit ball B in R 3
- 18.100B Problem Set 2 Due in class Tuesday, February 19. You may discuss the problems with other
- 18.700 nal review solutions I have not done these as carefully as I should; if you think something doesn't make sense,
- 18.104, Seminar in Analysis, Fall 2001 Meeting time: Tuesday and Thursday 11{12:30, room 2-151
- 18.700 Problem Set 4 Due in class Friday November 3; late work will not be accepted. Your work on
- 18.02A PROBLEM SET 9 Due in recitation Tuesday, February 10
- 18.700 Fall Semester, 2002 General Information
- 18.02A PROBLEM SET 10 Due in recitation Thursday, February 19
- The character table for E8 how we wrote down
- 18.440 Problem Set 4 Due in class Monday September 29; late work will not be accepted. You can
- 18.700 Problem Set 5 1. (8 points) Suppose A is a 3 3 real matrix. Prove that A has at
- noblackboxes The Orbit Method and Unitary Representations for Reductive Lie Groups Based on lectures at the European School of Group Theory
- 3. Hochschild-Serre spectral sequence for SL(3; R ) The rst big chart here is the E 1 term of the Hochschild-Serre spectral sequence for computing the
- 18.440 Problem Set 1 Due in class Monday September 3; late work will not be accepted. You can
- Representations of Lie Groups 18.758 The goal of this course is the classi cation of the (possibly in nite-dimensional) irreducible
- Unitary Representations and Complex Analysis David A. Vogan, Jr #
- 18.700 Problem Set 2 Due in class Friday October 6; late work will not be accepted. Your work on
- 18.781 Theory of Numbers Fall Semester, 2005 Class meetings: Monday, Wednesday, and Friday 2:00--3:00, in 2102.
- 4. LIE ALGEBRA COHOMOLOGY This is a quick-and-dirty introduction to Lie algebra cohomology. A reasonable
- Unitary Representations and Complex Analysis David A. Vogan, Jr
- Calculating Adams et al.
- 18.700 Problem Set 2 Due in class Thursday October 3; late work will not be accepted. Your work on
- Lexicographic order These notes are about an example that isn't directly relevant to the material in
- 18.104, Solutions to rst problem set Problem 1. Writing (a n ; b n ) for the nth row of the ladder, you had no diculty noticing the rules
- February 22, 2011 18.01 Problem Set 3 solutions
- 18.100B Problem Set 8 Due in class Wednesday, May 1. You may discuss the problems with other
- 2. HARMONIC ANALYSIS ON COMPACT GROUPS. These notes recall some general facts about Fourier analysis on a compact group
- Representations of Lie Groups 18.758 The goal of this course is the classification of the (possibly infinite-dimensional) irreducible
- 18.100B Problem Set 2 Due in class Tuesday, February 17. You may discuss the problems with other
- 1. Representations of SL(2; R) These notes describe the irreducible representations of the group G = SL(2; R) of two by two real
- 3. GEOMETRY OF FLAG MANIFOLDS AND REPRESENTATION THEORY.
- 18.737 Spring Semester, 2011 General Information
- 18.440 Probability and Random Variables Fall Semester, 2003 Class meetings: Monday, Wednesday, and Friday 2:00{3:00, in 4-163.
- Invariant measures on homogeneous spaces Since I screwed up a discussion of integration formulas in class on Monday, I have prepared
- The River for x2 I explained in class that you could solve Pell's equation x2
- February 17, 2011 18.01 Problem Set 3
- 18.02A PROBLEM SET 11 SOLUTIONS 1. (15 points) Let B be the unit ball in R 3
- 1. Representations of SL(2, R) These notes describe the irreducible representations of the group G = SL(2, R) of two by two real
- 18.781 Problem Set 4 Due Monday, October 3 in class.
- Translating Hermitian forms
- Finite maximal tori Department of Mathematics
- mathematics David Vogan
- BRANCHING TO A MAXIMAL COMPACT SUBGROUP DAVID A. VOGAN, JR.
- Branching to maximal compact
- 00 0000 0000 THE LOCAL LANGLANDS CONJECTURE David A. Vogan, Jr.
- CURRICULUM VITAE David A. Vogan, Jr.
- The character table for E8 David Vogan*
- 18.01, Spring Semester 2011 General Information
- February 3, 2010 18.01 Problem Set 1
- 18.01 Problem Set 1 Solutions Part II: 15 points
- February 11, 2010 18.01 Problem Set 2
- March 10, 2011 18.01 Problem Set 6
- 18.01 Problem Set 7 Solutions Part II: 15 points
- March 31, 2011 18.01 Problem Set 8
- March 31, 2011 18.01 Problem Set 7 Solutions
- April 1, 2011 18.01 Problem Set 9
- April 1, 2011 18.01 Problem Set 9 solutions
- May 2, 2011 18.01 Problem Set 11 solutions
- April 15, 2011 18.01 Problem Set 12
- May 2, 2011 18.01 Problem Set 12 Solutions
- Deforming subgroups This is a sketch of a solution of the homework assigned for March 17, to deform a
- 18.01, Spring Semester 2010 General Information
- 18.100B Problem Set 8 Due in class Monday, April 27. You may discuss the problems with other stu-
- 18.100B Problem Set 8 Partial Solutions 1. This is a version of problems 8 and 10 in the text (pages 166-167).
- 18.100B Problem Set 9 Due in class Monday, May 4. You may discuss the problems with other students,
- 1. Representations of SL(2, R) These notes describe the irreducible representations of the group G = SL(2, R) of two by two real
- 18.757 HW QUASI-ANSWERS 1. 1st Homework
- 2. HARMONIC ANALYSIS ON COMPACT GROUPS. These notes recall some general facts about Fourier analysis on a compact group
- 1. Homework 1 Problem 1. Write 2 or 3 sentences to explain why
- 18.034, Spring Semester 2006 General Information
- 18.034 Problem Set 5 Due Wednesday, March 22 in class.
- 18.034 Problem Set 8 Due Monday, May 1 in class.
- 18.781 Theory of Numbers Fall Semester, 2005 Class meetings: Monday, Wednesday, and Friday 2:003:00, in 2-102.
- 18.781 Problem Set 1 Due Monday, September 12 in class.
- 18.781 Problem Set 1 Due Monday, September 12 in class.
- 18.781 Problem Set 6 Due Monday, October 24 in class.
- 18.781 Problem Set 7 Due Monday, October 31 in class.
- SOLUTIONS TO HOMEWORK 7 1(a). The text offers a (pictorial) proof that division with remainder works in the
- 18.781 Problem Set 9 Due Monday, November 21 in class. There will be no problem set due on No-
- 18.781 Problem Set 10 solution supplement comments on problem 2
- 18.758 Supplementary Notes February 22, 2005
- 18.758 Supplementary Notes April 15, 2005
- 18.02A PROBLEM SET 10 Due in recitation Thursday, February 19
- 18.02A PROBLEM SET 11 Due in recitation Tuesday, February 24
- 18.02A PROBLEM SET 12 SOLUTIONS 1. (10 points) This problem is about the unit ball B in R3
- 18.02A Practice Questions Exam 7 The actual exam will be about 1/3 first two weeks, 2/3 last two weeks. Use the last two
- 18.034 Problem Set 9 Due Wednesday, May 10 in class.
- The size of infinite-dimensional
- SOLUTIONS TO HOMEWORK 8 Due Monday, November 8 in class. This looks longer than previous problem sets.
- 1. Homework 9 Problem. The Weyl algebra is the algebra of differential operators
- 18.440 Problem Set 3 Due in class Wednesday September 24; late work will not be accepted. You can
- April 15, 2011 18.01 Problem Set 10
- Invariant measures on homogeneous spaces Since I screwed up a discussion of integration formulas in class on Monday, I have prepared
- 18.01 Problem Set 4.5 UNASSIGNED PRACTICE Since I neglected to prepare a problem set due on March 9, these problems are intended to offer similar
- The method of coadjoint orbits for real reductive groups
- 18.440 Problem Set 6 Due in class Monday October 20; late work will not be accepted. You can discuss
- BRANCHING TO A MAXIMAL COMPACT SUBGROUP DAVID A. VOGAN, JR.
- 18.700 Problem Set 3 Due in class Thursday October 24; late work will not be accepted. Your work
- 18.440 Problem Set 9 Due in class Wednesday November 19; late work will not be accepted. You can
- 18.440 Problem Set 4 Due in class Monday September 29; late work will not be accepted. You can
- April 15, 2011 18.01 Problem Set 10 Solutions
- February 24, 2011 18.01 Problem Set 4
- Unitary representations of reductive Lie groups
- 18.034 Problem Set 2 Due Tuesday, February 21 in class.
- 18.781 Problem Set 2 Due Wednesday, September 21 in class.
- 18.034 Problem Set 4 Due Monday, March 6 in class.
- 18.100B Spring Semester, 2009 General Information
- SOLUTIONS TO HOMEWORK 9 1. Find a monic polynomial f(x) with integer coefficients such that
- SOLUTIONS TO HOMEWORK 5 1. You might remember from calculus Newton's method for finding roots of the
- 18.02A PROBLEM SET 12 Due in recitation Tuesday, March 9
- 18.100B Spring Semester, 2002 General Information
- Advanced Studies in Pure Mathematics 26, 1998 Analysis on Homogeneous Spaces and Representations of Lie Groups
- 18.700 Problem Set 5 Due in class Tuesday, November 26; late work will not be accepted. Your work
- The orbit method for reductive
- March 10, 2011 18.01 Problem Set 7
- 18.034 Problem Set 7 Due Wednesday, April 19 in class.
- February 21, 2011 18.01 Problem Set 2 solutions
- CURRICULUM VITAE David A. Vogan, Jr.
- 18.440 Problem Set 1 Due in class Monday September 3; late work will not be accepted. You can
- 18.440 Probability and Random Variables Fall Semester, 2003 Supplementary notes on continuous random variables
- 18.440 Probability and Random Variables Fall Semester, 2003 Class meetings: Monday, Wednesday, and Friday 2:00-3:00, in 4-163.
- 18.02A PROBLEM SET 9 Due in recitation Tuesday, February 10
- 4. LIE ALGEBRA COHOMOLOGY This is a quick-and-dirty introduction to Lie algebra cohomology. A reasonab*
- 00 0000 0000 THE LOCAL LANGLANDS CONJECTURE * David A. Vogan, Jr.
- 3. Hochschild-Serre spectral sequence for SL(3, R) The first big chart here is the E1 term of the Hochschild-Serre spectral seq*
- 18.700 final review problems I'll try to post some solutions Saturday 12/14.
- 18.700 Problem Set 4 Due in class Friday November 3; late work will not be accepted. Your work on
- 18.02A PROBLEM SET 12 SOLUTIONS 1. (10 points) This problem is about the unit ball B in R3
- References References
- 18.02A PROBLEM SET 11 SOLUTIONS 1. (15 points) Let B be the unit ball in R3
- UNITARY SHIMURA CORRESPONDENCES FOR SPLIT REAL GROUPS
- 18.700 Problem Set 1 Due in class Thursday September 19; late work will not be accepted. Your wo*
- 18.700 Problem Set 1 Due in class Friday September 22; late work will not be accepted. Your work
- Here are some practice problems you might use in preparing for the final exa* I'm sorry to say that I won't have a chance to post solutions to these problems
- 18.100B Problem Set 8 Due in class Wednesday, May 1. You may discuss the problems with other
- 18.700 Problem Set 3 Due in class Monday October 23; late work will not be accepted. Your work on
- The Langlands Classification and Irreducible Characters for Real Reductive Groups
- 18.100B Problem Set 9 Due in class Wednesday, May 8. You may discuss the problems with other
- 18.700 Problem Set 3 solutions 1. (10 points) Suppose a, b, c, and d are elements of a field F. Use
- 18.781 Theory of Numbers Fall Semester, 2005 Class meetings: Monday, Wednesday, and Friday 2:00-3:00, in 2-102.
- 18.700 Problem Set 1 Solutions 1. (10 points) In this problem the unknowns are called a0, a1, a2, and
- Unitary representations of reductive Lie groups
- 1. Representations of SL(2, R) These notes describe the irreducible representations of the group G = SL(2,*
- 18.700 Problem Set 2 Solutions Unless otherwise noted, the field of scalars is the real numbers.
- 18.700 final review solutions I have not done these as carefully as I should; if you think something does*
- 18.700 Problem Set 2 Due in class Friday October 6; late work will not be accepted. Your work on
- 1. Representations of SL(2, R) These notes describe the irreducible representations of the group G = SL(2,*
- 18.440 Problem Set 8 Due in class Wednesday November 12; late work will not be accepted. You can
- 18.700 Problem Set 4 Due in class Thursday November 7; late work will not be accepted. Your work
- Annals of Mathematics, 0 (1996), 1--67 On the classification of unitary
- 18.700 Problem Set 5 Due in class Monday November 20; late work will not be accepted. Your work
- 18.02A PROBLEM SET 9 SOLUTIONS 1. (10 points) The Lasker Rink in the northeast corner of Central Park is a perfect
- The Langlands Classification and Irreducible Characters for Real Reductive Groups
- SOLUTIONS TO HOMEWORK 9 1. Suppose that p and q are prime numbers, and m is an integer.
- 18.02A PROBLEM SET 11 SOLUTIONS 1. (15 points) Let B be the unit ball in R3
- UNITARY REPRESENTATIONS OF REDUCTIVE LIE GROUPS David A. Vogan, Jr.
- REPRESENTATION THEORY An Electronic Journal of the American Mathematical Society
- 18.01 Problem Set 6 Solutions Part II: 15 points
- Geometry and representations of
- 18.02A PROBLEM SET 13 SOLUTIONS 1. (10 points) This problem concerns an analogue of the theory of conservative*
- 18.440 Problem Set 7 Due in class Monday October 27; late work will not be accepted. You can dis*
- 18.100B Problem Set 4 Due in class Monday, March 11. You may discuss the problems with other
- Representations of Lie Groups 18.758 The goal of this course is to explain some of the ideas in the "local Langlan*
- 18.100B Problem Set 2 Due in class Tuesday, February 19. You may discuss the problems with other
- 18.440 Problem Set 9 Due in class Wednesday November 19; late work will not be accepted. You can
- Annals of Mathematics, 0 (1996), 1-67 On the classification of unitary
- Geometric quantization for nilpotent coadjoint orbits William Graham *
- 18.700 Problem Set 5 1. (8 points) Suppose A is a 3 x 3 real matrix. Prove that A has at
- 18.440 Problem Set 10 Due in class Friday December 5; late work will not be accepted. You can dis*
- The method of coadjoint orbits for real reductive groups
- 18.440 Problem Set 4 Due in class Monday September 29; late work will not be accepted. You can
- 18.700 Fall Semester, 2002 General Information
- 18.700 Problem Set 2 Due in class Thursday October 3; late work will not be accepted. Your work *
- Representations of Lie Groups 18.758 The goal of this course is the classification of the (possibly infinite-dime*
- Isolated unitary representations. David A. Vogan, Jr. *
- 18.781 Exam 2 Solutions Wednesday, November 9, 2005
- 18.104, Solutions to third problem set Problem 1. This asked for an algorithm like the one in problem 7 on page 10 for computing 2 1=3 . I'll
- 18.100B Problem Set 9 Due in class Wednesday, May 8. You may discuss the problems with other
- 18.02A PROBLEM SET 12 Due in recitation Tuesday, March 9
- 18.700 Problem Set 4 Due in class Thursday November 7; late work will not be accepted. Your work
- Lexicographic order These notes are about an example that isn't directly relevant to the material in
- Calculating Adams et al.
- SOLUTIONS TO HOMEWORK 2 Due Wednesday, September 21 in class.
- 18.02A PROBLEM SET 13 Due in recitation Tuesday, March 16
- 18.440 Problem Set 6 Due in class Monday October 20; late work will not be accepted. You can discuss
- 18.02A Second Half, Spring Semester 2004 General Information
- 18.781 Problem Set 8 Due Monday, November 7 in class. This looks longer than previous problem
- CORRECTIONS FOR LECTURES ON THE ORBIT METHOD, BY A.A. KIRILLOV.
- 18.02A PROBLEM SET 13 SOLUTIONS 1. (10 points) This problem concerns an analogue of the theory of conservative fields
- 18.440 Problem Set 8 Due in class Wednesday November 12; late work will not be accepted. You can
- Representations of Lie Groups 18.758 The goal of this course is to explain some of the ideas in the ``local Langlands conjectures.'' Since the
- 18.700 Problem Set 5 Due in class Tuesday, November 26; late work will not be accepted. Your work
- 18.02A PROBLEM SET 12 Due in recitation Tuesday, March 9
- Representations of Lie Groups 18.758 This will be an introduction to the infinite-dimensional unitary representa*
- Lexicographic order These notes are about an example that isn't directly relevant to the materi*
- 18.02A Second Half, Spring Semester 2004 General Information
- Proceedings of Symposia in Pure Mathematics Volume 00, 0000
- 18.02A PROBLEM SET 10 Due in recitation Thursday, February 19
- 18.440 Problem Set 3 Due in class Wednesday September 24; late work will not be accepted. You can
- 18.02A PROBLEM SET 11 Due in recitation Tuesday, February 24
- REPRESENTATION THEORY An Electronic Journal of the American Mathematical Society
- 18.100B Spring Semester, 2002 General Information
- 18.440 Problem Set 6 Due in class Monday October 20; late work will not be accepted. You can dis*
- 18.700 Problem Set 4 solutions 1. (15 points) Suppose that p and q are positive integers with p+q = n.
- Advanced Studies in Pure Mathematics 26, 1998 Analysis on Homogeneous Spaces and Representations of Lie Groups
- 18.700 Problem Set 3 Due in class Thursday October 24; late work will not be accepted. Your work
- 18.700 Problem Set 5 Due in class Monday November 20; late work will not be accepted. Your work
- 18.440 Problem Set 2 Due in class Monday September 15; late work will not be accepted. You can
- 18.02A PROBLEM SET 9 SOLUTIONS 1. (10 points) The Lasker Rink in the northeast corner of Central Park is a pe*
- 18.440 Problem Set 5 Due in class Monday October 6; late work will not be accepted. You can disc*
- CORRECTIONS FOR LECTURES ON THE ORBIT METHOD, BY A.A. KIRILLOV.
- BRANCHING TO A MAXIMAL COMPACT SUBGROUP DAVID A. VOGAN, JR.
- 18.02A PROBLEM SET 13 Due in recitation Tuesday, March 16
- 18.02A PROBLEM SET 10 SOLUTIONS 1. (10 points) A function f(x, y) of two variables is called harmonic if
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- Surveying the Challenge Reducing Memory Use
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- 4. LIE ALGEBRA COHOMOLOGY This is a quick-and-dirty introduction to Lie algebra cohomology. A reasonable
- Regular polyhedra and Coxeter
- 18.758 Supplementary Notes October 13, 2011
- KL polys for disconnected
- The character table for E8 how we wrote down
- mathematics David Vogan
- W-reps, nilp orbits, orbit method
- Regular polyhedra and Coxeter