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Birkhäuser

Lie Groups, Geometry, and Representation Theory

A Tribute to the Life and Work of Bertram Kostant

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  • © 2018

Overview

Editors:
  1. Victor G. Kac

    1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

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  2. Vladimir L. Popov

    1. Steklov Mathematical Institute, Moscow, Russia

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  • Celebrates one of the 20th century’s most significant mathematicians
  • Explores recent advances in topics that Kostant fundamentally influenced
  • Equips readers with an understanding of various subjects within Lie algebra and representation theory

Part of the book series: Progress in Mathematics (PM, volume 326)

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About this book

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 θ-groups (V. L. Popov)
  • Distributions on homogeneous spaces (N. Ressayre)
  • Reduction of orthogonal representations (J.-P. Serre)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Poisson Structures and Potentials

    • Anton Alekseev, Arkady Berenstein, Benjamin Hoffman, Yanpeng Li
    Pages 1-40

  3. Quasi-lisse Vertex Algebras and Modular Linear Differential Equations

    • Tomoyuki Arakawa, Kazuya Kawasetsu
    Pages 41-57

  4. On Dimension Growth of Modular Irreducible Representations of Semisimple Lie Algebras

    • Roman Bezrukavnikov, Ivan Losev
    Pages 59-89

  5. Remarks on the Asymptotic Hecke Algebra

    • Alexander Braverman, David Kazhdan
    Pages 91-108

  6. Autoequivalences of Tensor Categories Attached to Quantum Groups at Roots of 1

    • Alexei Davydov, Pavel Etingof, Dmitri Nikshych
    Pages 109-136

  7. Nil-Hecke Algebras and Whittaker 𝔇-Modules

    • Victor Ginzburg
    Pages 137-184

  8. Spectral Properties of Semi-classical Toeplitz Operators

    • V. Guillemin, A. Uribe, Z. Wang
    Pages 185-199

  9. Dual Kashiwara Functions for the B(∞) Crystal

    • Anthony Joseph
    Pages 201-233

  10. On Characters of Irreducible Highest Weight Modules of Negative Integer Level over Affine Lie Algebras

    • Victor G. Kac, Minoru Wakimoto
    Pages 235-252

  11. Alcoved Polytopes II

    • Thomas Lam, Alexander Postnikov
    Pages 253-272

  12. Representation Theory of Quantized Gieseker Varieties, I

    • Ivan Losev
    Pages 273-314

  13. Generalized Bruhat Cells and Completeness of Hamiltonian Flows of Kogan-Zelevinsky Integrable Systems

    • Jiang-Hua Lu, Yipeng Mi
    Pages 315-365

  14. On the Definition of Almost Characters

    • G. Lusztig
    Pages 367-379

  15. Verlinde Formulas for Nonsimply Connected Groups

    • Eckhard Meinrenken
    Pages 381-417

  16. Equivariant Index of Twisted Dirac Operators and Semi-classical Limits

    • Paul-`Emile Paradan, Mich`ele Vergne
    Pages 419-458

  17. Modality of Representations, and Packets for θ-Groups

    • Vladimir L. Popov
    Pages 459-479

  18. Distributions on Homogeneous Spaces and Applications

    • N. Ressayre
    Pages 481-526

  19. On the mod p reduction of orthogonal representations

    • Jean-Pierre Serre
    Pages 527-540
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Editors and Affiliations

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    Victor G. Kac

  • Steklov Mathematical Institute, Moscow, Russia

    Vladimir L. Popov

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