Representations of Rational Cherednik Algebras in Positive Characteristic

TL;DR

This paper investigates rational Cherednik algebras over fields of positive characteristic, establishing general properties of category O and explicitly computing characters of certain irreducible representations.

Contribution

It provides new results on the structure of category O and explicit character formulas for irreducible modules in positive characteristic settings.

Findings

General results about category O in positive characteristic

Explicit character formulas for trivial lowest weight irreducible representations

Analysis of Cherednik algebras related to finite linear groups

Abstract

We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational Cherednik algebras associated to the general and special linear group over a finite field of the same characteristic as the underlying algebraically closed field. For such algebras we calculate the characters of irreducible representations with trivial lowest weight.