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Lie groups, geometry, and representation theory : a tribute to the life and work of Bertram Kostant

Author: Victor G Kac; V L Popov; Bertram Kostant
Publisher: Cham, Switzerland : Birkhäuser, [2018]
Series: Progress in mathematics (Boston, Mass.), v. 326.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:

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  Read more...

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Genre/Form: Electronic books
Additional Physical Format: Print version:
(OCoLC)1051684346
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Victor G Kac; V L Popov; Bertram Kostant
ISBN: 9783030021917 3030021912
OCLC Number: 1080075415
Notes: 2.1 Braided tensor categories and their Picard groups
Description: 1 online resource
Contents: 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* 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 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 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
Series Title: Progress in mathematics (Boston, Mass.), v. 326.
Responsibility: Victor G. Kac, Vladimir L. Popov, editors.

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