Bethe subalgebras in Hecke algebra and Gaudin models
Quantum Algebra
2015-06-15 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1302.6495,
title = {Bethe subalgebras in Hecke algebra and Gaudin models},
author = {A. P. Isaev and Anatol N. Kirillov},
journal= {arXiv preprint arXiv:1302.6495},
year = {2015}
}