Howlett, Robert Brian - School of Mathematics and Statistics, University of Sydney

• 80/33A Semester 2 2000 The University of Sydney
• Introduction to Modern Algebra (Math2008) (Semester 2, 2003)
• AUTOMORPHISMS OF NEARLY FINITE COXETER GROUPS W. N. FRANZSEN AND R. B. HOWLETT
• Metric Spaces Lecture 24 The familiar Intermediate Value Theorem of elementary calculus says that if a real
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2902 Vector Spaces
• Group representation theory Lecture 19, 13/10/97 Proposition. Let H, K be subgroups of the finite group G, and let : H C
• Week 1 Summary Number Theory is concerned mainly with properties of integers. In particular,
• Week 10 Summary The following proposition is proved by exactly the same argument used to prove
• Group representation theory Lecture 17, 24/9/97 Proposition. If : FG Matd(F) is a representation of a group algebra FG then the restric-
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2008 Introduction to Modern Algebra
• It will be convenient to make use of the following notation: if d and m are integers "d | m" means "d is a divisor of m".
• The University of Sydney MATH2902 Vector Spaces
• Summary of week 9 (Lectures 25, 26 and 27) Lecture 25 and the first part of Lecture 26 were concerned with permutations.
• Summary of week 5 (lectures 13, 14 and 15) Lectures 13 and 14 saw the conclusion of Chapter 4 of [VST]. First, Theo-
• Geometry of solitons Graeme Segal
• Group representation theory Lecture 5, 11/8/97 Suppose that a group G has an action on a set S. For variety, we shall assume that this is a right
• The University of Sydney Pure Mathematics 3901
• The University of Sydney MATH2008 Introduction to Modern Algebra
• INDUCING W-GRAPHS II ROBERT B. HOWLETT AND YUNCHUAN YIN
• The University of Sydney Pure Mathematics 3901
• Summary of week 2 (lectures 4, 5 and 6) Lecture 4 was concerned with the concept of linearity. This material appears
• The University of Sydney Pure Mathematics 3901
• INDUCED W-GRAPHS ROBERT B. HOWLETT AND YUNCHUAN YIN
• Metric Spaces Lecture 18 The Contraction Mapping Theorem
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2902 Vector Spaces
• Week 5 Summary Let , Z[i]. We shall that divides , which we write as |, if = for
• Week 12 Summary In this lecture we shall prove the Law of Quadratic Reciprocity. We follow the
• THE UNIVERSITY OF Introduction
• The University of Sydney MATH2902 Vector Spaces
• Metric Spaces Lecture 22 Topological spaces were invented because they provide a natural context in which
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2008 Introduction to Modern Algebra
• Group representation theory Lecture 9, 25/8/97 The calculation from last lecture showed that
• The University of Sydney MATH2902 Vector Spaces
• Group representation theory Lecture 15, 15/9/97 Before moving on to more theory, let us calculate some examples. Unfortunately, verifying elegant
• The University of Sydney Pure Mathematics 3901
• Group representation theory Lecture 11, 1/9/97 In Lecture 10 we described the regular representation of G as the linear representation derived
• The Fundamental Theorem of Algebra Let f(z) = 0 +1z +2z2
• The University of Sydney MATH Pure Mathematics 3901
• Group representation theory Lecture 16, 17/9/97 Definition. Let F be a field. An F-algebra is a vector space A over F equipped with an operation
• Metric Spaces Lecture 25 Definition. A subset S of a metric space X is said to be sequentially compact if every
• Projection onto a line through the origin Suppose that a
• Metric Spaces Lecture 1 Introduction
• The University of Sydney Pure Mathematics 3901
• The University of Sydney MATH2902 Vector Spaces
• Metric Spaces Lecture 3 Examples of metric spaces
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney Pure Mathematics 3901
• 80/27 Semester 1, 2000 Page 1 of 2 page attachment Attachment to Examination Paper (Semester 1, 2000)
• Week 8 Summary Example: Given that 81 =
• Metric Spaces Lecture 8 Uniform and pointwise convergence
• J. Symbolic Computation (2000) 11, 1000 Matrix generators for exceptional groups of Lie type
• (i) R := RealField(); V := VectorSpace(R,5);
• The University of Sydney Pure Mathematics 3901
• Group Theory Group theory is the mathematical study of symmetry. This statement will be clarified
• ON REFLECTION LENGTH IN REFLECTION GROUPS R.B. Howlett and G.I. Lehrer
• On Klyachko's model for the representations of finite general linear groups
• PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
• ON REGULARITY OF FINITE REFLECTION GROUPS R. B. Howlett
• The University Automorphisms of Coxeter groups
• An undergraduate course in Abstract Algebra
• Bob Howlett Group representation theory Lecture 1, 28/7/97 Introduction
• The group S4, consisting of all permutations of {1, 2, 3, 4}, has 24 elements. It has a subgroup K = {(1 2)(3 4), (1 3)(2 4), (1 4)(2 3)}, and another subgroup L = {(1 2), (1 3), (2 3), (1 2 3), (1 3 2)},
• Group representation theory Lecture 3, 4/8/97 As several people pointed out after last lecture, my description of the representation of the quater-
• Group representation theory Lecture 6, 13/8/97 The First Isomorphism Theorem Let V and W be G-modules and let f: V W be a G-
• Group representation theory Lecture 18, 8/10/97 Modules and representations of algebras
• The University of Sydney MATH3906 Representation Theory
• Vector Space Theory A course for second year students by
• Robert B. Howlett Chapter 1: Symmetry
• MATH3010 Information Theory Lectures and Tutorials
• 80/60 Semester 2 2003 Seat Number
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• The University of Sydney MATH2008 Introduction to Modern Algebra
• In general terms, our aim in this first part of the course is to use vector space theory to study the geometry of Euclidean space. A good knowledge of the subject matter of the
• Normal subgroups Let G be a group and K a subgroup of G. If t G then we define
• If G is a group and x, y G then it is not necessarily true that xy = yx. If x and y do satisfy this condition we say that they commute. For example, the elements (1, 2)
• Metric Spaces Lecture 2 The definition of continuity (as stated in Lecture 1 for functions from R2
• Metric Spaces Lecture 6 Let (X, U) be a topological space. Recall from Lecture 5 that if A1 and A2 are subsets
• Metric Spaces Lecture 10 Let C be the set of all continuous real-valued functions on the closed interval [0, 1].
• Metric Spaces Lecture 15 Subspace topology
• Metric Spaces Lecture 17 Homeomorphisms
• Metric Spaces Lecture 19 Picard's Theorem
• Metric Spaces Lecture 20 To end our section on completeness, we give one more application of the Contraction
• Metric Spaces Lecture 21 Recall that a subset A if a metric space X is said to be bounded if there exists a
• Metric Spaces Lecture 23 We noted last time that a space that is homeomorphic to a connected space is also
• The University of Sydney Pure Mathematics 3901
• The University of Sydney Pure Mathematics 3901
• The University of Sydney Pure Mathematics 3901
• The University of Sydney Pure Mathematics 3901
• The University of Sydney Pure Mathematics 3901
• Week 2 Summary Suppose that r0 and r1 are nonnegative integers, not both zero. Choose the
• Week 4 Summary The least common multiple of two nonzero integers a and b is a positive integer
• Week 6 Summary We have shown that if a and b are integers such that a2
• Week 7 Summary Suppose that p and q are integers with gcd(p, q) = 1 (so that the fraction p/q is
• Week 11 Summary Let p be an odd prime, and define (as in Lecture 19)
• Summary of week 4 (lectures 10, 11 and 12) We have seen that if F is any field then Fn
• Summary of week 6 (lectures 16, 17 and 18) Every complex number can be uniquely expressed in the form = a + bi,
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2902 Vector Spaces
• Symmetric groups and related algebras Gordon James
• Dominoes, Eulerian Circuits, and Spanning Trees Brendan D McKay, Australian National University (speaker)
• The University of Sydney Faculties of Arts and Science
• Group representation theory Lecture 7, 18/8/97 From now on, unless otherwise stated, the scalar field for each vector space we deal with will be C,
• Summary of week 7 (lectures 19, 20 and 21) Recall that if A is an np matrix over the field R then the column space of A,
• The University of Sydney MATH3906 Representation Theory
• The University of Sydney Pure Mathematics 3901
• Sylow's Theorem The term "modern algebra" principally refers to abstract theories in which the objects
• The homology of symmetric groups and the algebra of covering spaces Andre Joyal (speaker) and Terrence Bisson
• Congruences on the integers Definition. Let n be a positive integer. Integers a and b are said to be congruent
• Abstract inner product spaces Definition An inner product space is a vector space V over the real field R equipped
• Metric Spaces Lecture 13 The completion of a metric space
• The University of Sydney MATH2902 Vector Spaces
• The University of Sydney MATH2902 Vector Spaces
• Metric Spaces Lecture 7 Lemma. Let x = (x1, x2, . . . , xn) and y = (y1, y2, . . . , yn) be points in Rn
• Week 3 Summary The rule for finding the continued fraction expansion of a number is this. Find
• The University of Sydney MATH2008 Introduction to Modern Algebra
• Group representation theory Lecture 13, 8/9/97 Let us review the situation we have been discussing in the last few lectures. Given a finite group
• Group representation theory Lecture 21, 20/10/97 Let D and D be diagrams corresponding to partitions and of n. It is clear that the set
• The University of Sydney MATH2068 Number Theory and Cryptography
• Week 9 Summary Let n1, n2, . . . , nk be positive integers. The direct sum of Zn1 , Zn2 . . . , Znk
• Metric Spaces Lecture 11 Every set of real numbers which has an upper bound has a supremum (least upper
• Summary of week 8 (Lectures 22, 23 and 24) This week we completed our discussion of Chapter 5 of [VST].
• Summary of week 11 (Lectures 31, 32 and 33) The contents of this week's lectures coincided almost exactly with Chapter 7
• Metric Spaces Lecture 5 Definition. Let S be a set and U a collection of subsets of S. We call U a topology for
• Metric Spaces Lecture 14 We have yet to prove the first part of the important theorem that was discussed
• 80/27 Semester 1, 2000 Page 1 of 3 THE UNIVERSITY OF SYDNEY
• Isomorphism Definition. Let G and H be groups. A function f: G H is called an isomorphism if
• Projections using orthogonal bases We showed last time that if {a
• Metric Spaces Lecture 16 Product topology
• On the integral group algebra of a finite algebraic group R. B. Howlett and G. I. Lehrer
• The homology of symmetric groups and the algebra of covering spaces
• On Harish-Chandra induction and restriction for modules of Levi subgroups
• On the Schur multipliers of Coxeter groups Robert B. Howlett
• Symmetric groups and related algebras Gordon James
• Metric Spaces Lecture 26 A comment on separation properties
• THE UNIVERSITY OF SYDNEY MATH3962 Rings, Fields and Galois Theory(A)
• Parity of permutations Given a permutation of {1, 2, . . . , n}, draw a diagram consisting of two horizontal
• Summary of week 3 (lectures 7, 8 and 9) Lecture 7 commenced with an example similar to #7 on p. 41 of [VST]: solving
• The University of Sydney MATH2902 Vector Spaces
• * | Springer-Verlag | *__ ||Mathematische Annalen ||
• Dominoes, Eulerian Circuits, and Spanning Trees Brendan D McKay, Australian National University (speaker)
• Metric Spaces Lecture 12 It is natural to ask under what circumstances is a subspace of a complete space
• The University of Sydney MATH2902 Vector Spaces
• ASSIGNMENT COVER SHEET This cover sheet must be stapled to the front of your assignment, inside the folder.
• Metric Spaces Lecture 4 Induced metric
• More on permutations Recall that a permutation of {1, 2, . . . , n} is uniquely determined by specifying what
• Summary of week 12 (Lectures 34, 35 and 36) We have defined the right null space of A Mat(m n, F) to be the space
• Sylow's Theorem The term "modern algebra" principally refers to abstract theories in which the objects
• The University of Sydney MATH2902 Vector Spaces
• Geometry of Solitons Graeme Segal
• Metric Spaces Lecture 9 Some examples of topological spaces
• 8038 Semester 2 2007 The University of Sydney
• THE UNIVERSITY OF Polynomial congruences modulo a prime
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2988 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• THE UNIVERSITY OF Roots of unity modulo a prime
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2988 Number Theory and Cryptography (Adv)
• 8038 Semester 2 2005 The University of Sydney
• THE UNIVERSITY OF Discrete Logarithms
• 8036 Semester 2 2008 The University of Sydney
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• 8038 Semester 2 2006 The University of Sydney
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• The University of Sydney MATH2068 Number Theory and Cryptography
• 8036 Semester 2 2010 The University of Sydney
• 8036 Semester 2 2009 The University of Sydney
• THE UNIVERSITY OF Computing discrete logarithms
• 8038 Semester 2 2005 The University of Sydney
• The University of Sydney MATH2068 Number Theory and Cryptography