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Dedicated to Anthony Joseph in honor of his 60th birthday, this volume contains two articles reviewing different aspects of Joseph's impact on the theory of representations of Lie algebras and 17 original contributions from leading specialists in the field. The book contains new results on different aspects of Lie theory, including Lie superalgebras, quantum groups, crystal bases, representations of reductive groups in finite characteristic, and the geometric Langlands program.
List of contents
From the contents:
- Preface
- List of Publications
- List of Students
- Tribute Speech Transcript
- Tribute Letter
- Review Papers: W. Mc.Govern: The Work of Anthony Joseph in Classical Representation Theory
- D. Farkas and G. Letzter: Quantized Representation Theory Following Joseph
- Research Papers: J. Alev and F. Dumas: Operateurs differentiels invariants et problème de Noether
- A. Beilinson: Langlands parameters for Heisenberg modules
- A. Braverman and P. Etingoff: Instanton counting via affine Lie algebras II: from Whittaker vectors to the Seiberg Witten prepotential
- I. Cherednik: Irreducibility of perfect representations of double affine Hecke algebras
- D. Gaitsgory and D. Kazhdan: Algebraic groups over a 2-dimensional local field: some further constructions
- M. Kashiwara, P. Schapira, F. Ivorra, and I. Waschkies: Microlocalization of Ind-sheaves
- D. Kazhdan and Ya. Varshavsky: On endoscopic decomposition of certain depth zero representations
- A. Kirillov and L. Rybnikov: Odd family algebras
- B. Kostant and N. Wallach: G_Z theory from the perspective of classical mechanics I
- S. Kumar and K.-H. Neeb: Extensions of Algebraic Groups
- T. Levasseur and T. Stafford: Differential Operators and Cohomology Groups on the Basic Affine Space
- G. Lusztig: A q-analogue of an identity of N.Wallach
- L. Makar-Limanov: On centralizers in the quantum plane algebra
- M. Nazarov and A. Sergeev: Centralizer construction of the Yangian of the queer Lie superalgebra
Summary
Dedicated to Anthony Joseph, this volume contains surveys and invited articles by leading specialists in representation theory. The focus here is on semisimple Lie algebras and quantum groups, where the impact of Joseph's work has been seminal and has changed the face of the subject.
Two introductory biographical overviews of Joseph's contributions in classical representation theory (the theory of primitive ideals in semisimple Lie algebras) and quantized representation theory (the study of the quantized enveloping algebra) are followed by 16 research articles covering a number of varied and interesting topics in representation theory.
