Lie Groups, Geometry, and Representation Theory: A Tribute to the Life and Work of Bertram Kostant: 326 (Progress in Mathematics, 326) - Hardcover

Hardcover

ISBN 10: 3030021904 ISBN 13: 9783030021900

Publisher: Birkhäuser, 2018

Synopsis

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)
  

About this title

From the Back Cover

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 categoriesand 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)
  

Edition details

• Publisher: Birkhäuser
• Publication date: 2018
• Language: English
• ISBN 10: 3030021904
• ISBN 13: 9783030021900
• Binding: Hardcover
• Edition number: 1
• Number of pages: 552
• Editor: Kac Victor G., Popov Vladimir L.