A family of Weyl group representations
speaker: Eric Sommers (U of Massachusetts at Amherst)abstract: We will discuss a family of representations of a Weyl group that arises in different contexts: hyperplane arrangements, affine Springer theory, and rational Cherednik algebras. The focus of the talk will be on decomposing a graded version of these representations into induced pieces and using this to obtain q-analogues of the values of hyperplane characteristic polynomials, evaluated at certain positive integers. This yields q-analogues of well-known combinatorial quantities (namely, the Kreweras and Narayana numbers) that satsify the cyclic sieving property with respect to various subposets of the W-noncrossing partitions (joint work with Vic Reiner). If time permits, we will discuss implications for the double-graded version of this story, which relates to work of Haiman, Hikita, and others.
timetable:
Mon 13 Jun, 16:15 - 17:30, Aula Bianchi Scienze
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