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" Lie groups, geometry, and representation theory : "
Victor G. Kac, Vladimir L. Popov, editors.
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BL
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859707
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| Title & Author
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Lie groups, geometry, and representation theory : : a tribute to the life and work of Bertram Kostant /\ Victor G. Kac, Vladimir L. Popov, editors.
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| Publication Statement
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Cham, Switzerland :: Birkhäuser,, [2018]
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| Series Statement
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Progress in mathematics ;; volume 326
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1 online resource
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| ISBN
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3030021912
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: 9783030021917
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3030021904
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9783030021900
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| Notes
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2.1 Braided tensor categories and their Picard groups
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| Contents
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Intro; Contents; A Tribute to Bertram Kostant; Poisson Structures and Potentials; 1 Introduction; 2 Positivity theory; 2.1 Algebraic tori and positive maps; 2.2 Tropicalization of positive maps; 2.3 Positive varieties; 3 Potentials; 4 Potentials on double Bruhat cells; 4.1 Semisimple groups; 4.2 Positive structures on double Bruhat cells; 4.3 Cluster variables on double Bruhat cells; 4.4 Weakly estimate-dominated functions on double Bruhat cells; 5 Positive Poisson varieties; 5.1 Definition of positive Poisson varieties; 5.2 Poisson algebraic groups; 5.3 The positive Poisson variety G*
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4.6 Proof of (2) of Theorem 1.15 Application to W-algebras; 5.1 Background on W-algebras; 5.2 Restriction functor for HC-bimodules; 5.3 Results on finite-dimensional irreducible W-modules; 5.4 Reduction of representations mod p; 5.5 Proof of Theorem 5.2; 5.6 Proof of Corollary 5.3; 6 Application to real variation of stability conditions; References; Remarks on the Asymptotic Hecke Algebra; 1 Introduction and statement of the results; 1.1 Notation; 1.2 Matrix Paley-Wiener theorem; 1.4 Harish-Chandra algebra; 1.5 Tempered representations; 1.7 Asymptotic Hecke algebra; 1.10 An algebraic version
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6 Tropicalization of Poisson structures6.1 Real forms of Poisson structures; 6.2 Real forms of positive Poisson varieties; 6.3 Partial tropicalization; 6.4 Partial tropicalization of K*; References; Quasi-lisse Vertex Algebras and Modular Linear Differential Equations; 1 Introduction; 2 Quasi-lisse vertex algebras; 3 A necessary condition for the quasi-lisse property; 4 Finiteness of ordinary representations; 5 Modular linear differential equations; 6 Examples of quasi-lisse vertex algebras; 7 The characters of affine vertex algebras associated with the Deligne exceptional series; References
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On Dimension Growth of Modular Irreducible Representations of Semisimple Lie Algebras1 Introduction; 2 Preliminaries; 2.1 Harish-Chandra bimodules and primitive ideals; 2.2 Hecke algebras, cells, and HC-bimodules; 2.3 Localization in characteristic p; 3 Lengths; 3.1 Reduction of HC-bimodules to characteristic p; 3.2 Results on growth of lengths; 3.3 Lengths for HC-bimodules; 3.4 Lengths in characteristic p; 4 Proof of Theorem 1.1; 4.1 Proof of part (1) of Theorem 1.1; 4.2 Outline of the proof of (2) of Theorem 1.1; 4.3 Etingof's construction; 4.4 Proof of Proposition 4.2; 4.5 Degeneration map
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| Abstract
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This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 - February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant's fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of?-groups (V.L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre).
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Lie groups.
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Representations of Lie groups.
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Lie groups.
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Representations of Lie groups.
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Topological Groups, Lie Groups.
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Differential Geometry.
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Group Theory and Generalizations.
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Polytopes.
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| Dewey Classification
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512/.482
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| LC Classification
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QA387.L54 2018
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| Added Entry
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Kac, Victor G.,1943-
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Kostant, Bertram
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Popov, V. L., (Vladimir Leonidovich)
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