Gaudin model and Deligne-Mumford compactification

Leonid Rybnikov (Higher School of Economics, Moscow)

Tuesday 21st May 16:00-17:00 Maths 311B

Abstract

Gaudin model is a completely integrable quantum spin chain which depends on a n-tuple of pairwise distinct point on the complex line. According to Aguirre, Felder and Veselov, this family of integrable systems extends (by including some degenerations) to a family of quantum integrable systems parametrised by the Deligne-Mumford moduli space of stable rational curves. I will discuss the monodromy of solutions of the corresponding Bethe ansatz equations along this moduli space. This monodromy is given by combinatorial Schutzenberger involutions (or, equivalently, by commutors of Kashiwara crystals).

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