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Title:
Bethe subalgebras and Kirillov-Reshetikhin crystals
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Abstract:
Bethe subalgebras form a family of maximal commutative subalgebras of the Yangian of a simple Lie algebra, parametrized by regular elements of the corresponding adjoint Lie group. We introduce an affine (Kirillov-Reshetikhin) crystal structure on the set of eigenlines for a Bethe subalgebra in a representation of the Yangian (under certain conditions on the representation, satisfied by all tensor products of fundamental representations in types A and C). This helps to describe the monodromy of solutions of Bethe ansatz for the corresponding XXX Heisenberg magnet chain. This is a joint project with Inna Mashanova-Golikova and Vasily Krylov.
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