Studies in Lie Theory

by Bernstein, Joseph; Hinich, Vladimir; Melnikov, Anna

• ISBN13: 9780817643423
• ISBN10: 0817643427
• Format: Hardcover
• Copyright: 2006-03-01
• Publisher: Birkhauser

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.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

Preface	p. ix
Publications of Anthony Joseph	p. xiii
Students of Anthony Joseph	p. xxi
From Denise Joseph	p. xxiii
From Jacques Dixmier: A Recollection of Tony Joseph	p. xxv
Survey and Review	p. 1
The work of Anthony Joseph in classical representation theory	p. 3
Quantized representation theory following Joseph	p. 9
Research Articles
Operateurs differentiels invariants et probleme de Noether	p. 21
Langlands parameters for Heisenberg modules	p. 51
Instanton counting via affine Lie algebras II: From Whittaker vectors to the Seiberg-Witten prepotential	p. 61
Irreducibility of perfect representations of double affine Hecke algebras	p. 79
Algebraic groups over a 2-dimensional local field: Some further constructions	p. 97
Modules with a Demazure flag	p. 131
Microlocalization of ind-sheaves	p. 171
Endoscopic decomposition of certain depth zero representations	p. 223
Odd family algebras	p. 303
Gelfand-Zeitlin theory from the perspective of classical mechanics. I	p. 319
Extensions of algebraic groups	p. 365
Differential operators and cohomology groups on the basic affine space	p. 377
A q-analogue of an identity of N. Wallach	p. 405
Centralizers in the quantum plane algebra	p. 411
Centralizer construction of the Yangian of the queer Lie superalgebra	p. 417
Definitio nova algebroidis verticiani	p. 443
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