Topics course 280, Kazhdan-Lusztig Theory: Hecke Algebras and Orthogonal Polynomials RFG

Spring 2005

Meeting:	This topics course meets Mondays at 12:30-2pm in 593 Kerr NOTE the time CHANGE Wednesdays at 3:30 - 5pm in 593 Kerr during the Spring Quarter.
Instructor:	Monica Vazirani, Kerr Hall 579, phone: 752-2218, vazirani@math.ucdavis.edu
CRN:	72780
Office Hours:	tba
Grading:	Students who plan to attend regularly (missing no more than 3? classes) and participate in the discussion and who will present a paper in class can register for three credits.
Web:	http://www.math.ucdavis.edu/~vazirani/S05/280.html

Course description

This reading seminar runs in the context of the Research Focus Group on "Hecke Algebras and Orthogonal Polynomials".
We will read and discuss topics of mutual interest.
In the paper Representations of Coxeter groups and Hecke algebras; Invent. Math. 53 (1979), no. 2, 165--184; by Kazhdan and Lusztig, they explained many combinatorial phenomena that are associated to a Weyl group W in different contexts. The key discovery uses a set of certain polynomials (Kazhdan-Lusztig polynomials) which are the coefficients expressing the KL basis in terms of a more standard basis .
A list of texts and papers we will be following/reading/hearing are linked here. Go look and try to pick a paper SOON!!

A list of suggested homework exercises are listed here.

Schedule Spring

April 4 -- MV on where KL polys appear. (some of the Brenti and Goodman papers give a nice overview)
April 6 -- MV on defn of KL poly and R polys (read along in Humphreys or the intros of many of the papers listed)
Apr 9-- (notice Saturday, April 09 is the bay area discrete math day).
Do think about attending. If you are interested in carpooling there, please email monica.
April 11-- uniqueness
April 13-- existence. starting on cells or inverse KL polys
April 18-- more on cells (and if we haven't already, inverse KL polys)
April 20-- parabolic KL polys
April 25-- moving toward quantum groups and the frenkel-khovanov-kirillov paper
April 27-- maybe Philip Sternberg on quantum groups, representation theory and canonical bases
May 2--, sl_\infty, U_q(\hat sl_n) and its action on Fock space
May 4-- Fock space, and its global basis
May 9-- Fock space
May 11-- the FKK paper and canonical bases
May 16-- NOT MV; MV will be out of town. (ncsu conf) someone volunteer ??!
May 18-- NOT MV; MV will be out of town. (ncsu conf) someone volunteer ??!
May 23-- cancelled for the sake of the berkeley RTG conferece.
May 25-- MV on the LLT and goodman/wenzl algorithm. (was horribly unprepared and did an awful job-- sorry on that. hope to rectify it.)
May 30-- MEMORIAL DAY. holiday. whoopee.
June 1-- Chris Berg on Brenti's paper.
June 6-- James Parmenter.
June 8-- Isaiah Lankham on Billey/Warrington paper (last day)

Email list: the people who now receive emails about this course are listed here. If you are NOT on this list and would like to be (or if you ARE on the list and would like to be removed), please email monica.
anne@math berg@math capnjim@math deka@math endelman@math issy@math lesyoung@math sternberg@math svis@math vazirani@math wilmarth@math