Representations of Rational Cherednik Algebras in Positive Characteristic

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.

Cited by in corpus (12)

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• Invariants of GL_n(F_q) in polynomials mod Frobenius powers
• Poincare-Birkhoff-Witt Theorems
• Representations of rational Cherednik algebras of G(m,r,n) in positive characteristic
• The polynomial representation of the type $A_{n-1}$ rational Cherednik algebra in characteristic $p\mid n$
• Drinfeld Hecke algebras for symmetric groups in positive characteristic
• A Poincare-Birkhoff-Witt theorem for quadratic algebras with group actions
• Representations of Cherednik Algebras Associated to Symmetric and Dihedral Groups in Positive Characteristic
• The Hilbert Series of the Irreducible Quotient of the Polynomial Representation of the Rational Cherednik Algebra of Type $A_{n-1}$ in Characteristic $p$ for $p|n-1$
• PBW deformations of skew group algebras in positive characteristic
• Group-twisted Alexander-Whitney and Eilenberg-Zilber maps
• The Rational Cherednik Algebra of Type $A_1$ with Divided Powers