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Progress in Mathematics

Lie Groups, Geometry, and Representation Theory

A Tribute to the Life and Work of Bertram Kostant

Editors: Kac, Victor G., Popov, Vladimir (Eds.)

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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
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eBook $109.00
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  • ISBN 978-3-030-02191-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-030-02190-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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)

Table of contents (18 chapters)

Table of contents (18 chapters)
  • Poisson Structures and Potentials

    Alekseev, Anton (et al.)

    Pages 1-40

  • Quasi-lisse Vertex Algebras and Modular Linear Differential Equations

    Arakawa, Tomoyuki (et al.)

    Pages 41-57

  • On Dimension Growth of Modular Irreducible Representations of Semisimple Lie Algebras

    Bezrukavnikov, Roman (et al.)

    Pages 59-89

  • Remarks on the Asymptotic Hecke Algebra

    Braverman, Alexander (et al.)

    Pages 91-108

  • Autoequivalences of Tensor Categories Attached to Quantum Groups at Roots of 1

    Davydov, Alexei (et al.)

    Pages 109-136

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-030-02191-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-030-02190-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lie Groups, Geometry, and Representation Theory
Book Subtitle
A Tribute to the Life and Work of Bertram Kostant
Editors
  • Victor G. Kac
  • Vladimir Popov
Series Title
Progress in Mathematics
Series Volume
326
Copyright
2018
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-02191-7
DOI
10.1007/978-3-030-02191-7
Hardcover ISBN
978-3-030-02190-0
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XII, 540
Topics