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

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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. Th
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Longest Weyl Group Elements in Actionprojective system. In type .., the group .. is related to reduced Burau representations, and in general to complex reflection groups. Behavior of the longest Weyl group elements in .. is studied in detail. The results will be used in the analysis by Li (in preparation) of graded/cyclic quiver variet
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Lusztig’s ,-Analogue of Weight Multiplicity via Crystals. In finite type .., we rederive the description of the generalized exponents in terms of crystal graphs without using the combinatorics of semistandard tableaux or the charge statistic. In finite type .., we obtain a combinatorial description of the generalized exponents based on the so-called dist
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Evaluation Modules for Quantum Toroidal , Algebras respect to the homogeneous grading, where .. = .. and .. We discuss . evaluation modules. We give highest weights of evaluation highest weight modules. We also obtain the decomposition of the evaluation Wakimoto module with respect to a Gelfand–Zeitlin-type subalgebra of a completion of ., which de
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Book 2021the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of
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