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Bethe subalgebras of the group algebra of the symmetric group

arXiv:1004.4248

Abstract

We introduce families of maximal commutative subalgebras, called Bethe subalgebras, of the group algebra of the symmetric group. Bethe subalgebras are deformations of the Gelfand-Zetlin subalgebra. We describe various properties of Bethe subalgebras.

AmsLaTeX, 32 pages; references updated