Finite dimensional representations of double affine Hecke algebra of rank 1

TL;DR

This paper classifies all finite-dimensional representations of the double affine Hecke algebra of type C^vee C_1 when q is not a root of unity, advancing understanding of its algebraic structure.

Contribution

It provides a complete classification of finite-dimensional representations for this specific algebra in the generic case, which was previously unknown.

Findings

Complete classification of finite-dimensional representations

Results applicable when q is not a root of unity

Enhanced understanding of algebraic structure

Abstract

We classify the finite dimensional representations of the double affine Hecke algebra of type $C^{\vee}C_1$ in the case when $q$ is not a root of 1.