Bethe subalgebras in Hecke algebra and Gaudin models

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.

References in corpus (1)

• Functional equations for transfer-matrix operators in open Hecke chain models

Cited by in corpus (7)

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• Induced representations and traces for chains of affine and cyclotomic Hecke algebras
• Markov traces on affine and cyclotomic Yokonuma-Hecke algebras
• Remarks towards the spectrum of the Heisenberg spin chain type models
• Fusion procedure for Degenerate cyclotomic Hecke algebras