The polynomial representation of the type $A_{n-1}$ rational Cherednik algebra in characteristic $p\mid n$

Abstract

We study the polynomial representation of the rational Cherednik algebra of type $A_{n-1}$ with generic parameter in characteristic $p$ for $p\mid n$. We give explicit formulas for generators for the maximal proper graded submodule, show that they cut out a complete intersection, and thus compute the Hilbert series of the irreducible quotient. Our methods are motivated by taking characteristic $p$ analogues of existing characteristic $0$ results.

8 pages. v3: Streamlined proof of complete intersection property in Section 3; main results are unchanged

References in corpus (2)

• Representations of Rational Cherednik Algebras in Positive Characteristic
• Representations of rational Cherednik algebras of G(m,r,n) in positive characteristic

Cited by in corpus (1)

• Drinfeld Hecke algebras for symmetric groups in positive characteristic