A_N-type Dunkl operators and new spin Calogero-Sutherland models

TL;DR

This paper introduces a new family of Dunkl operators that preserve polynomial subspaces, leading to the development of novel exactly and quasi-exactly solvable spin Calogero-Sutherland models, including elliptic Hamiltonians.

Contribution

It constructs a new family of Dunkl operators and derives several new solvable quantum spin models, expanding the class of integrable systems in mathematical physics.

Findings

New Dunkl operators preserving polynomial subspaces

Multiple new exactly and quasi-exactly solvable models

Introduction of elliptic spin Hamiltonians

Abstract

A new family of A_N-type Dunkl operators preserving a polynomial subspace of finite dimension is constructed. Using a general quadratic combination of these operators and the usual Dunkl operators, several new families of exactly and quasi-exactly solvable quantum spin Calogero-Sutherland models are obtained. These include, in particular, three families of quasi-exactly solvable elliptic spin Hamiltonians.