Studies in Lie Theory

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  • Format: Hardcover
  • Copyright: 2006-03-01
  • Publisher: Birkhauser

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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.Contributors: J. Alev; A. Beilinson; A. Braverman; I. Cherednik; J. Dixmier; F. Dumas; P. Etingof; D. Farkas; D. Gaitsgory; F. Ivorra; A. Joseph; D. Joseph; M. Kashiwara; D. Kazhdan; A.A. Kirillov; B. Kostant; S. Kumar; G. Letzter; T. Levasseur; G. Lusztig; L. Makar-Limanov; W. McGovern; M. Nazarov; K-H. Neeb; L.G. Rybnikov; P. Schapira; V. Schechtman; A. Sergeev; J.T. Stafford; Ya. Varshavsky; N. Wallach; and I. Waschkies.

Table of Contents

Prefacep. ix
Publications of Anthony Josephp. xiii
Students of Anthony Josephp. xxi
From Denise Josephp. xxiii
From Jacques Dixmier: A Recollection of Tony Josephp. xxv
Survey and Reviewp. 1
The work of Anthony Joseph in classical representation theoryp. 3
Quantized representation theory following Josephp. 9
Research Articles
Operateurs differentiels invariants et probleme de Noetherp. 21
Langlands parameters for Heisenberg modulesp. 51
Instanton counting via affine Lie algebras II: From Whittaker vectors to the Seiberg-Witten prepotentialp. 61
Irreducibility of perfect representations of double affine Hecke algebrasp. 79
Algebraic groups over a 2-dimensional local field: Some further constructionsp. 97
Modules with a Demazure flagp. 131
Microlocalization of ind-sheavesp. 171
Endoscopic decomposition of certain depth zero representationsp. 223
Odd family algebrasp. 303
Gelfand-Zeitlin theory from the perspective of classical mechanics. Ip. 319
Extensions of algebraic groupsp. 365
Differential operators and cohomology groups on the basic affine spacep. 377
A q-analogue of an identity of N. Wallachp. 405
Centralizers in the quantum plane algebrap. 411
Centralizer construction of the Yangian of the queer Lie superalgebrap. 417
Definitio nova algebroidis verticianip. 443
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