Arc spaces and DAHA representations

TL;DR

This paper explores the relationship between finite-dimensional representations of type A rational Cherednik algebras and differential forms on moduli spaces linked to plane curve singularities, revealing new connections in algebraic geometry and representation theory.

Contribution

It establishes a comparison between multiplicity spaces in Cherednik algebra representations and differential forms on specific moduli spaces, providing novel insights into their structure.

Findings

Identifies a correspondence between representation multiplicities and differential forms.

Connects algebraic representations with geometric structures of plane curve singularities.

Enhances understanding of the classification of Cherednik algebra representations.

Abstract

A theorem of Y. Berest, P. Etingof and V. Ginzburg states that finite dimensional irreducible representations of a type A rational Cherednik algebra are classified by one rational number m/n. Every such representation is a representation of the symmetric group S_n. We compare certain multiplicity spaces in its decomposition into irreducible representations of S_n with the spaces of differential forms on a zero-dimensional moduli space associated with the plane curve singularity x^m=y^n.