Finite dimensional representations of DAHA and affine Springers fibers : the spherical case

TL;DR

This paper classifies finite-dimensional simple spherical representations of rational double affine Hecke algebras and explores a notable family of such representations in double affine Hecke algebras.

Contribution

It provides a classification of finite-dimensional simple spherical representations and investigates a significant family within double affine Hecke algebras.

Findings

Classification of finite-dimensional simple spherical representations

Identification of a remarkable family of representations

Insights into the structure of affine Springer fibers

Abstract

We classify finite dimensional simple spherical representations of rational double affine Hecke algebras, and we study a remarkable family of finite dimensional simple spherical representations of double affine Hecke algebras.