GAUDIN HAMILTONIANS GENERATE THE BETHE ALGEBRA OF A TENSOR POWER OF THE VECTOR REPRESENTATION OF glN
نویسنده
چکیده
It is shown that the Gaudin Hamiltonians H1, . . . , Hn generate the Bethe algebra of the n-fold tensor power of the vector representation of glN . Surprisingly, the formula for the generators of the Bethe algebra in terms of the Gaudin Hamiltonians does not depend on N . Moreover, this formula coincides with Wilson’s formula for the stationary Baker–Akhiezer function on the adelic Grassmannian. §
منابع مشابه
Bethe Subalgebras in Hecke Algebra and Gaudin Models Bethe Subalgebras in Hecke Algebra and Gaudin Models
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.
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