Finite dimensional representations of the rational Cherednik algebra for $G_4$

TL;DR

This paper classifies all irreducible finite dimensional representations of the rational Cherednik algebra for the complex reflection group G_4 and computes their characters, advancing understanding of these algebraic structures.

Contribution

It provides a complete classification of finite dimensional irreducible representations and their characters for the rational Cherednik algebra of G_4, a novel result in the field.

Findings

Complete classification of finite dimensional irreducible representations.

Explicit computation of characters for these representations.

Enhanced understanding of the structure of the rational Cherednik algebra for G_4.

Abstract

In this paper, we study representations of the rational Cherednik algebra associated to the complex reflection group $G_4$. In particular, we classify the irreducible finite dimensional representations and compute their characters.