Category O for the rational Cherednik algebra associated to the complex reflection group G_12

TL;DR

This paper characterizes the irreducible representations in category O of the rational Cherednik algebra for the complex reflection group G_12, including finite-dimensional cases and their characters.

Contribution

It provides a detailed description of irreducible representations and character computations for the rational Cherednik algebra associated with G_12, for arbitrary parameters.

Findings

Classification of irreducible representations in category O

Explicit determination of finite-dimensional representations

Character formulas for these representations

Abstract

In this paper, we describe the irreducible representations in category O of the rational Cherednik algebra H_c(G_12,h) associated to the complex reflection group G_12 with reflection representation h for an arbitary complex parameter c. In particular, we determine the irreducible finite dimensional representations and compute their characters.