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Lie Groups, Geometry, and Representation Theory

A Tribute to the Life and Work of Bertram Kostant

Victor G. Kac (Hrsg.), Vladimir L. Popov (Hrsg.)

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Naturwissenschaften, Medizin, Informatik, Technik / Arithmetik, Algebra

Beschreibung

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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Schlagwörter

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