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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Tuesday, May 3, 2016 - 3:00pm

Arun Ram

University of Melbourne

Location

Drexel University

Korman Center 245

A parking function is a sequence (b_1, a*|, b_n) of positive integers which, when rearranged in increasing order (a_1\le a_2\le a*|\le a_n), is such that a_i\le i. I will first convert parking functions to elements of the affine Weyl group which correspond to regions of the Shi hyperplane arrangement and bases of a module for the rational Cherednik algebra (or double affine Hecke algebra). As explained, for example, in papers of Varagnolo- Vasserot and Oblomkov-Yun, this module can be realized as the cohomology (or K-theory) of an affine Springer fiber. These bases are closely connected to Macdonald polynomials. Goresky-Kotwitz- Macpherson explain how to chop up the affine Springer fiber into tractable pieces indexed by the (generalised) parking functions (paving by Hessenbergs). Ia**ll start by drawing the pictures and then explain how to read the connections off the picture.