Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
A combinatorial proof of Macdonald positivity University of California, Berkeley
 

Summary: A combinatorial proof of Macdonald positivity
Sami Assaf
University of California, Berkeley
sassaf@math.upenn.edu
Banff International Research Station
September 10, 2007
S. Assaf - A combinatorial proof of Macdonald positivity p.1/20
Macdonald positivity
In 1988, Macdonald defined H(x; q, t) and proved it to be
symmetric. Writing H(x; q, t) = K,(q, t)s(x), he
conjectured:
Theorem. (Haiman 2001) We have K,(q, t) N[q, t].
Original proof realizes H(x; q, t) as the Frobenius series of
doubly graded Sn-module (Garsia-Haiman module) using
algebraic geometry of the Hilbert scheme.
Newer proof due to Grojnowski and Haiman relates
H(x; q, t) to LLT positivity (Haglund's formula) and then
uses Kazhdan-Lusztig theory.
Problem: Find a combinatorial proof of positivity.
S. Assaf - A combinatorial proof of Macdonald positivity p.2/20

  

Source: Assaf, Sami H. - Department of Mathematics, Massachusetts Institute of Technology (MIT

 

Collections: Mathematics