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Algebra and Combinatorics Seminar by Chelsea Drescher
Wednesday, Oct. 23, 2019
2:30 p.m. - 3:30 p.m. Location: SLC 1.204

Chelsea Drescher

University of North Texas

Invariants of modular reflection groups and Hilbert series

A clever way to show an object is an integer or exhibits integer coefficients is to prove that it is counting something seemingly unrelated. For example, one may verify that various generalizations of Catalan numbers are polynomials with integer coefficients by exhibiting them as series counting dimensions of certain invariant spaces. These invariant spaces arise in the representation theory of rational Cherednik algebras for Coxeter and complex reflection groups. In this talk, we discuss a modular analogue and consider some reflection groups acting in positive characteristic. We consider a 2017 conjecture by Lewis, Reiner, and Stanton on invariants of the general linear group GL(n,q) and (q,t)-binomial coefficients. We discuss a solution to the local case of this conjecture, when the reflection group acting fixes one mirror hyperplane. Over fields of characteristic zero, these groups are cyclic, but they are more complicated when the characteristic of the underlying field divides the order of the group.

Persons with disabilities may submit a request for accommodations to participate in this event at UT Dallas' ADA website. You may also call (972) 883-5331 for assistance or send an email to [email protected]. All requests should be received no later than 2 business days prior to the event.
Contact Info:
Carlos Arreche, 972-883-6594
Questions? Email me.

Tagged as Lectures/Seminars, Professional Dev.
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