Category O for Rational Cherednik Algebras H_{t,c}(GL_2(F_p),h) in Characteristic p

TL;DR

This paper characterizes the irreducible objects in category O for rational Cherednik algebras associated with GL_2(F_p) over fields of positive characteristic p, covering all parameter values.

Contribution

It provides a comprehensive description of the characters of irreducible objects in category O for these algebras in characteristic p, for any t and generic c.

Findings

Characters of irreducible objects explicitly described

Results hold for all t and generic c in characteristic p

Advances understanding of category O in positive characteristic

Abstract

In this paper we describe the characters of irreducible objects in category O for the rational Cherednik algebra associated to GL_2(F_p) over an algebraically closed field of positive characteristic p, for any value of the parameter t and generic value of the parameter c.