Ebook: New Developments in Lie Theory and Their Applications
- Tags: Topological Groups Lie Groups, Group Theory and Generalizations
- Series: Progress in Mathematics 105
- Year: 1992
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
Representation theory, and more generally Lie theory, has played a very important role in many of the recent developments of mathematics and in the interaction of mathematics with physics. In August-September 1989, a workshop (Third Workshop on Representation Theory of Lie Groups and its Applications) was held in the environs of C6rdoba, Argentina to present expositions of important recent developments in the field that would be accessible to graduate students and researchers in related fields. This volume contains articles that are edited versions of the lectures (and short courses) given at the workshop. Within representation theory, one of the main open problems is to determine the unitary dual of a real reductive group. Although this prob lem is as yet unsolved, the recent work of Barbasch, Vogan, Arthur as well as others has shed new light on the structure of the problem. The article of D. Vogan presents an exposition of some aspects of this prob lem, emphasizing an extension of the orbit method of Kostant, Kirillov. Several examples are given that explain why the orbit method should be extended and how this extension should be implemented.
Content:
Front Matter....Pages i-ix
Automorphic Forms....Pages 1-25
Analytic and Geometric Realization of Representations....Pages 27-47
Introduction to Quantized Enveloping Algebras....Pages 49-65
The Vanishing of Scalar Curvature on 6 Manifolds, Einstein’s Equation, and Representation Theory....Pages 67-86
Unitary Representations of Reductive Lie Groups and the Orbit Method....Pages 87-114
Twistor Theory for Riemannian Manifolds....Pages 115-128
You Can’t Hear the Shape of a Manifold....Pages 129-146
Kuznetsov Formulas....Pages 147-154
Lefschetz Numbers and Cyclic Base Change for Purely Imaginary Extensions....Pages 155-161
Some Zeta Functions Attached to ?G/K....Pages 163-177
On the Centralizer of K in the Universal Enveloping Algebra of SO(n, 1) and SU(n, 1)....Pages 179-186
On Spherical Modules....Pages 187-198
Generalized Weil Representations for SL(n,k), n odd, k a Finite Field....Pages 199-206
Local Multiplicity of the Intersection of Lagrangian Cycles and the Index of Holonomic Modules....Pages 207-225
Back Matter....Pages 227-228
Content:
Front Matter....Pages i-ix
Automorphic Forms....Pages 1-25
Analytic and Geometric Realization of Representations....Pages 27-47
Introduction to Quantized Enveloping Algebras....Pages 49-65
The Vanishing of Scalar Curvature on 6 Manifolds, Einstein’s Equation, and Representation Theory....Pages 67-86
Unitary Representations of Reductive Lie Groups and the Orbit Method....Pages 87-114
Twistor Theory for Riemannian Manifolds....Pages 115-128
You Can’t Hear the Shape of a Manifold....Pages 129-146
Kuznetsov Formulas....Pages 147-154
Lefschetz Numbers and Cyclic Base Change for Purely Imaginary Extensions....Pages 155-161
Some Zeta Functions Attached to ?G/K....Pages 163-177
On the Centralizer of K in the Universal Enveloping Algebra of SO(n, 1) and SU(n, 1)....Pages 179-186
On Spherical Modules....Pages 187-198
Generalized Weil Representations for SL(n,k), n odd, k a Finite Field....Pages 199-206
Local Multiplicity of the Intersection of Lagrangian Cycles and the Index of Holonomic Modules....Pages 207-225
Back Matter....Pages 227-228
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