Lie Groups, Geometry, and Representation Theory
A Tribute to the Life and Work of Bertram Kostant
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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 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)
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)
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
Autor*in
Victor G. Kac
Themen in »Lie Groups, Geometry, and Representation Theory«
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 Whittaker modules Orbit method