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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.…mehr
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.
Joseph Bernstein, Tel Aviv University, Tel Aviv, Israel / Vladimir Hinich, University of Haifa, Israel / Anna Melnikov, University of Haifa, Israel
Inhaltsangabe
Survey and Review.- The work of Anthony Joseph in classical representation theory.- Quantized representation theory following Joseph.- Research Articles.- Opérateurs différentiels invariants et problème de Noether.- Langlands parameters for Heisenberg modules.- Instanton counting via affine Lie algebras II: From Whittaker vectors to the Seiberg-Witten prepotential.- Irreducibility of perfect representations of double affine Hecke algebras.- Algebraic groups over a 2-dimensional local field: Some further constructions.- Modules with a Demazure flag.- Microlocalization of ind-sheaves.- Endoscopic decomposition of certain depth zero representations.- Odd family algebras.- Gelfand-Zeitlin theory from the perspective of classical mechanics. I.- Extensions of algebraic groups.- Differential operators and cohomology groups on the basic affine space.- A q-analogue of an identity of N. Wallach.- Centralizers in the quantum plane algebra.- Centralizer construction of the Yangian of the queer Lie superalgebra.- Definitio nova algebroidis verticiani.
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
Survey and Review.- The work of Anthony Joseph in classical representation theory.- Quantized representation theory following Joseph.- Research Articles.- Opérateurs différentiels invariants et problème de Noether.- Langlands parameters for Heisenberg modules.- Instanton counting via affine Lie algebras II: From Whittaker vectors to the Seiberg-Witten prepotential.- Irreducibility of perfect representations of double affine Hecke algebras.- Algebraic groups over a 2-dimensional local field: Some further constructions.- Modules with a Demazure flag.- Microlocalization of ind-sheaves.- Endoscopic decomposition of certain depth zero representations.- Odd family algebras.- Gelfand-Zeitlin theory from the perspective of classical mechanics. I.- Extensions of algebraic groups.- Differential operators and cohomology groups on the basic affine space.- A q-analogue of an identity of N. Wallach.- Centralizers in the quantum plane algebra.- Centralizer construction of the Yangian of the queer Lie superalgebra.- Definitio nova algebroidis verticiani.
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
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