Bethe subalgebras in Hecke algebra and Gaudin models

TL;DR

This paper constructs Bethe subalgebras within Hecke algebras, linking them to Gaudin models via transfer-matrix operators, and introduces a non-local analogue of Gaudin Hamiltonians.

Contribution

It introduces a new construction of Bethe subalgebras in Hecke algebras and connects them to Gaudin models through a classical limit and transfer-matrix operators.

Findings

Bethe subalgebras are generated via Sklyanin's transfer-matrix.

Gaudin Hamiltonians are derived in the classical limit q -> 1.

A non-local analogue of Gaudin Hamiltonians is constructed for Hecke algebras.

Abstract

The generating function for elements of the Bethe subalgebra of Hecke algebra is constructed as Sklyanin's transfer-matrix operator for Hecke chain. We show that in a special classical limit q -> 1 the Hamiltonians of the Gaudin model can be derived from the transfer-matrix operator of Hecke chain. We consruct a non-local analogue of the Gaudin Hamiltonians for the case of Hecke algebras.