Titlebook: Representation Theory, Mathematical Physics, and Integrable Systems; In Honor of Nicolai Anton Alekseev,Edward Frenkel,Milen Yakimov Book

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,Quantum Periodicity and Kirillov–Reshetikhin Modules,We give a proof of the periodicity of quantum .-systems of type .. × .. with certain spiral boundary conditions. Our proof is based on the categorification of the .-system in terms of the representation theory of quantum affine algebras, more precisely on relations between classes of Kirillov–Reshetikhin modules and of evaluation modules.

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A Note on the E-Polynomials of a Stratification of the Hilbert Scheme of Points,The stratification associated with the number of generators of the ideals of the punctual Hilbert scheme of points on the affine plane has been studied since the 1970s. In this paper, we present an elegant formula for the E-polynomials of these strata.

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,Irreducibility of the Wysiwyg Representations of Thompson’s Groups,We prove irreducibility and mutual inequivalence for certain unitary representations of R. Thompson’s groups F and T.

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Tensor Product of the Fock Representation with Its Dual and the Deligne Category,We describe .-module structure of the tensor product of the Fock representation and its shifted dual using action of . on the abelian envelope of the Deligne’s category .(.).

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https://doi.org/10.1007/978-3-030-78148-4Quantum Groups; Representation Theory; Categorifications; Kac-Moody Algebras; Invariants of knots and 3-