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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

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Anton Alekseev, Arkady Berenstein, Benjamin Hoffman, Yanpeng Li
    Pages 1-40
  3. Tomoyuki Arakawa, Kazuya Kawasetsu
    Pages 41-57
  4. Alexander Braverman, David Kazhdan
    Pages 91-108
  5. Alexei Davydov, Pavel Etingof, Dmitri Nikshych
    Pages 109-136
  6. Victor Ginzburg
    Pages 137-184
  7. V. Guillemin, A. Uribe, Z. Wang
    Pages 185-199
  8. Thomas Lam, Alexander Postnikov
    Pages 253-272
  9. G. Lusztig
    Pages 367-379
  10. Eckhard Meinrenken
    Pages 381-417
  11. Paul-`Emile Paradan, Mich`ele Vergne
    Pages 419-458

About this book

Introduction

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)

Keywords

Bertram Kostant Transformation groups Lie groups Representation theory Bert Kostant Kac-Moody algebra Jacobson-Morozov theorem Amtisur-Levitski identity Hochschild-Kostant-Rosenberg isomorphism Hochschild homology Weyl group Kostant separation theorem Lie algebra Representation theory Whittaker modules Orbit method Grassmann algebra Nilpotent orbit

Editors and affiliations

  • Victor G. Kac
    • 1
  • Vladimir L. Popov
    • 2
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Steklov Mathematical InstituteMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-02191-7
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-02190-0
  • Online ISBN 978-3-030-02191-7
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site