Abstract
The generating function for elements of the Bethe subalgebra of the Hecke algebra is constructed as Sklyanin’s transfer-matrix operator for the Hecke chain. We show that in a special classical limit \({q \to 1}\) the Hamiltonians of the Gaudin model can be derived from the transfer-matrix operator of the Hecke chain. We construct a non-local analog of the Gaudin Hamiltonians in the case of the Hecke algebras.
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The work of A.P. Isaev was supported by the grant RFBR 11-01-00980-a and grant Higher School of Economics No. 11-09-0038.
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Isaev, A.P., Kirillov, A.N. Bethe Subalgebras in Hecke Algebra and Gaudin models. Lett Math Phys 104, 179–193 (2014). https://doi.org/10.1007/s11005-013-0660-3
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DOI: https://doi.org/10.1007/s11005-013-0660-3