SL2(R) / by Serge Lang.

By: Material type: TextTextSeries: Graduate texts in mathematics ; 105.Publisher: New York, NY : Springer New York, 1985Copyright date: ©1985Description: 428 pages 33 illustrationsContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
Subject(s): Additional physical formats: SL2(R); No titleDDC classification:
  • 512 23
LOC classification:
  • QA150-272
Contents:
I. General Results -- II. Compact Groups -- III. Induced Representations -- IV. Spherical Functions -- V. The Spherical Transform -- VI. The Derived Representation on the Lie Algebra -- VII. Traces -- VIII. The PlanchereS Formula -- IX. Discrete Series -- X. Partial Differential Operators -- XI. The Weil Representation -- XII. Representation on 0L2(...\G) -- XIII. The continuous Part of L2(...\G) -- XIV. Spectral Decomposition of the Laplace Operator on L\s -- Appendix 1. Bounded Hermitian Operators and Schur's Lemma -- 1. Continuous functions of operators -- 2. Projection functions of operators -- Appendix 2. Unbounded Operators -- 1. Self-adjoint operators -- 2. The spectral measure -- 3. The resolvant formula -- Appendix 3. Meromorphic Families of Operators -- 1. Compact operators -- 2. Bounded operators -- Appendix 4. Elliptic PDF -- 1. Sobolev spaces -- 2. Ordinary estimates -- 3. Elliptic estimates -- 4. Compactness and regularity on the torus -- 5. Regularity in Euclidean space -- Appendix 5. Weak and Strong Analyticity -- 1. Complex theorem -- 2. Real theorem.
Summary: SL2(R) gives the student an introduction to the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). This field is of interest not only for its own sake, but for its connections with other areas such as number theory, as brought out, for example, in the work of Langlands. The rapid development of representation theory over the past 40 years has made it increasingly difficult for a student to enter the field. This book makes the theory accessible to a wide audience, its only prerequisites being a knowledge of real analysis, and some differential equations.
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I. General Results -- II. Compact Groups -- III. Induced Representations -- IV. Spherical Functions -- V. The Spherical Transform -- VI. The Derived Representation on the Lie Algebra -- VII. Traces -- VIII. The PlanchereS Formula -- IX. Discrete Series -- X. Partial Differential Operators -- XI. The Weil Representation -- XII. Representation on 0L2(...\G) -- XIII. The continuous Part of L2(...\G) -- XIV. Spectral Decomposition of the Laplace Operator on L\s -- Appendix 1. Bounded Hermitian Operators and Schur's Lemma -- 1. Continuous functions of operators -- 2. Projection functions of operators -- Appendix 2. Unbounded Operators -- 1. Self-adjoint operators -- 2. The spectral measure -- 3. The resolvant formula -- Appendix 3. Meromorphic Families of Operators -- 1. Compact operators -- 2. Bounded operators -- Appendix 4. Elliptic PDF -- 1. Sobolev spaces -- 2. Ordinary estimates -- 3. Elliptic estimates -- 4. Compactness and regularity on the torus -- 5. Regularity in Euclidean space -- Appendix 5. Weak and Strong Analyticity -- 1. Complex theorem -- 2. Real theorem.

SL2(R) gives the student an introduction to the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). This field is of interest not only for its own sake, but for its connections with other areas such as number theory, as brought out, for example, in the work of Langlands. The rapid development of representation theory over the past 40 years has made it increasingly difficult for a student to enter the field. This book makes the theory accessible to a wide audience, its only prerequisites being a knowledge of real analysis, and some differential equations.

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