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Topics in Combinatorial Representation Theory |
| March 17, 2008 to March 21, 2008 |
| Organized By: Sergey Fomin, Bernard Leclerc, Vic Reiner (Chair), Monica Vazirani |
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| Parent Programs: |
| Combinatorial Representation Theory |
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| Return to Workshop Description |
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LLT polynomials
Thursday March 20, 2008
02:00PM - 03:00PM
Speakers:
Mark Haiman
Abstract:
I'll speak about my recent joint work with Grojnowski, in
which we interpret the coefficients of the combinatorially defined
q-symmetric polynomials of Lascoux, Leclerc and Thibon (LLT) as matrix
coefficients of the operator of multiplication by a Kazhdan-Lusztig
basis element, with respect to a certain hybrid of the standard and
Kazhdan-Lusztig bases of the affine Hecke algebra. This leads to a
proof of the positivity conjecture for LLT polynomials and to a
natural definition and corresponding positivity theorem for LLT
polynomials associated to any root system.
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