Browsing by Author "Feigin, Boris"

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    Finite Type Modules and Bethe Ansatz Equations
    (Springer, 2017-08) Feigin, Boris; Jimbo, Michio; Miwa, Tetsuji; Mukhin, Eugene; Department of Mathematical Sciences, School of Science
    We introduce and study a category OfinbObfin of modules of the Borel subalgebra UqbUqb of a quantum affine algebra UqgUqg, where the commutative algebra of Drinfeld generators hi,rhi,r, corresponding to Cartan currents, has finitely many characteristic values. This category is a natural extension of the category of finite-dimensional UqgUqg modules. In particular, we classify the irreducible objects, discuss their properties, and describe the combinatorics of the q-characters. We study transfer matrices corresponding to modules in OfinbObfin. Among them, we find the Baxter QiQi operators and TiTi operators satisfying relations of the form TiQi=∏jQj+∏kQkTiQi=∏jQj+∏kQk. We show that these operators are polynomials of the spectral parameter after a suitable normalization. This allows us to prove the Bethe ansatz equations for the zeroes of the eigenvalues of the QiQi operators acting in an arbitrary finite-dimensional representation of UqgUqg.
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    Quantum Toroidal Comodule Algebra of Type A(n-1) and Integrals of Motion
    (Foundation Compositio Mathematica, 2022-07-07) Feigin, Boris; Jimbo, Michio; Mukhin, Evgeny; Mathematical Sciences, School of Science
    We introduce an algebra Kn which has a structure of a left comodule over the quantum toroidal algebra of type An−1. Algebra Kn is a higher rank generalization of K1, which provides a uniform description of deformed W algebras associated with Lie (super)algebras of types BCD. We show that Kn possesses a family of commutative subalgebras.