Finite-difference representations of the degenerate affine Hecke algebra

TL;DR

This paper introduces finite-difference representations of the degenerate affine Hecke algebra, analyzes related lattice Hamiltonians via Bethe-Ansatz, and explores connections to Yangian representations and the 1-d Hubbard Model.

Contribution

It presents novel finite-difference representations of the degenerate affine Hecke algebra and links them to spin Calogero-Sutherland Hamiltonians and Yangian structures.

Findings

Finite-difference representations of the degenerate affine Hecke algebra are constructed.

Lattice analogues of spin Calogero-Sutherland Hamiltonians are analyzed using Bethe-Ansatz.

Connections between $sl(m)$-Yangian representations and the 1-d Hubbard Model are established.

Abstract

The representations of the degenerate affine Hecke algebra in which the analogues of the Dunkl operators are given by finite-difference operators are introduced. The non-selfadjoint lattice analogues of the spin Calogero-Sutherland hamiltonians are analysed by Bethe-Ansatz. The $ sl(m)$-Yangian representations arising from the finite-difference representations of the degenerate affine Hecke algebra are shown to be related to the Yangian representation of the 1-d Hubbard Model.