The finite-dimensional representations of the rational Cherednik algebra of $E_8$ when $c=1/3$

TL;DR

This paper completes the classification of finite-dimensional irreducible representations of rational Cherednik algebras for exceptional Coxeter groups by resolving the last open case involving the group E8 at parameter c=1/3.

Contribution

It provides the final classification for the E8 case of rational Cherednik algebras with equal parameters, specifically when c=1/3.

Findings

Complete classification of finite-dimensional irreducible representations for E8 at c=1/3

Resolved the last open case in the classification for exceptional Coxeter groups

Advances understanding of rational Cherednik algebras in complex reflection groups

Abstract

We finish the classification of finite-dimensional irreducible representations of rational Cherednik algebras $H_c(W)$ with equal parameters for exceptional Coxeter groups by resolving the last open case: when $W=E_8$ and the denominator of $c$ is $3$.