Titlebook: Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification; In honor of Vyjayant Jacob Greenstein

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Conormal Varieties on the Cominuscule Grassmannianer show that this compactification is a Schubert subvariety of .(.) if and only if .(...)???.∕. is smooth, where .. is the longest element in the Weyl group of .. This result is applied to compute the conormal fibre at the zero matrix in any determinantal variety.

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Jacob Greenstein,David Hernandez,Prasad SenesiExamines representation theory as connected with affine Lie algebras and their quantum analogues.Presents a broad view of the area, including mini-courses, surveys, and original research.Celebrates th

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Quantum Affine Algebras and Cluster Algebrasgton. The aim of the minicourse, consisting of three lectures, was to present a number of results and conjectures on certain monoidal categories of finite-dimensional representations of quantum affine algebras, obtained by exploiting the fact that their Grothendieck rings have the natural structure of a cluster algebra.

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Categorical Representations and Classical ,-Adic Groupsarameters and of the characteristic). This reduces the classification of simple objects to computing a representation previously introduced by Enomoto and Kashiwara. We did this in some particular cases.

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Formulae of ,-Divided Powers in ,, IIs (also known as the .-divided powers) for the coideal subalgebra of the quantum . were established by Bao and Wang. We establish closed formulae for the .-divided powers as polynomials in . and also in terms of Chevalley generators of the quantum . when the parameter . is an arbitrary .-integer. The formulae were known earlier when .?=?0, 1.

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