Representations of Cherednik Algebras Associated to Symmetric and Dihedral Groups in Positive Characteristic

Abstract

We consider irreducible lowest-weight representations of Cherednik algebras associated to certain classes of complex reflection groups in characteristic p. In particular, we study maximal graded submodules of Verma modules associated to these algebras. Various results and conjectures are presented concerning generators of these maximal submodules, which are found by computing singular polynomials of Dunkl operators.

added PBW theorem in section 2

References in corpus (5)

• Lecture notes on Cherednik algebras
• Representations of Rational Cherednik Algebras in Positive Characteristic
• Reducibility of the polynomial representation of the degenerate double affine Hecke algebra
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• On some representations of the rational Cherednik algeba

Cited by in corpus (1)

• Drinfeld Hecke algebras for symmetric groups in positive characteristic