Titlebook: Lie Groups, Geometry, and Representation Theory; A Tribute to the Lif Victor G. Kac,Vladimir L. Popov Book 2018 Springer Nature Switzerland

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Limpid

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On Dimension Growth of Modular Irreducible Representations of Semisimple Lie Algebras,cisely, it is known that for . ≫ 0, the irreducibles with a regular rational central character λ and .-character χ are indexed by a certain canonical basis in the . of the Springer fiber of χ. This basis is independent of .. For a basis element, the dimension of the corresponding module is a polynom

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Antioxidant

Alcoved Polytopes II,nd also compatible definitions of hypersimplices, descent numbers and major index for all Weyl groups. We give a .-analogue of Weyl’s formula for the order of the Weyl group. For ., . and ., we give a Gröobner basis which induces the triangulation of alcoved polytopes.

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Representation Theory of Quantized Gieseker Varieties, I,l parameters and categories . for special values of parameters. We find the values of parameters, where the quantizations have finite homological dimension, and we establish the abelian localization theorem.We classify two-sided ideals. Finally, we determine the annihilators of the irreducible objec