SL2（R）

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作　者：	（美）莱恩著
出版社：	世界图书出版公司
丛编项：
标　签：	组合理论

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ISBN：	9787510004544	出版时间：	2009-08-01	包装：	平装
开本：	24开	页数：	428	字数：

内容简介

　　Starting with Bargmanns paPer on the tnhmte dimenslonal representattons olSL2（R），the theory of representations of semisimple Lie groups has evolved toa rather extensive production.Some of the main contributors have been：Gelfand-Naimark and Harish-Chandra.who considered the Lorentz group inthe late forties；Gelfand-Nalmark.who dealt with the classical complexgroups.while Harish·Chandra worked out the general reaI case。especiallythrough the derived representation of the Lie algebra.establishing thePlancherel formula （Gclfand-Graev also contributed to the teal case）；Cat-tan。Gelfand-Naimark.Godement.Harish.Chandra。who developed thetheory of spherical functions （Godement gave several Bourbaki seminarreports giving proofs for a number of spectral results not accessible other-wise）；Selberg，who took the group modulo a discrete subgroup and obtainedthe trace formula；Gelfand.Fomin，Piateckii.Shapiro，and Harish.Chandra，who established connections with automorphic forms；Jacquet-Lanlands，who pushed through the connection with L-series and Hecke.

作者简介

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图书目录

Notation
Chapter Ⅰ General Results
　1 The representation on Co(G)
　2 A criterion for complete reducibility
　3 L2 kernels and operators
　4 Plancherel measures
Chapter Compact Groups
　l Decomposition over K for SL2(R)
　2 Compact groups in general
Chapter Ⅲ Induced Representations
　1 Integration on coset spaces
　2 Induced representations
　3 Associated spherical functions
　4 The kernel defining the induced representation
Chapter Ⅳ Spherical Functions
　1 Bi-invariance
　2 Irreducibility
　3 The spherical property
　4 Connection with unitary representations
　5 Positive definite functions
Chapter Ⅴ The Spherical Transform
　2 The Harish transform
　3 The Mellin transform
　4 The spherical transform
　5 Explicit formulas and asymptotic expansions
Chapter Ⅵ The Derived Representation on the Lie Algebra
　1 The derived representation
　2 The derived representation decomposed over K
　3 Unitarization of a representation
　4 The Lie derivatives on G
　5 Irreducible components of the induced representations
　6 Classification of all unitary irreducible representations
　7 Separation by the trace
Chapter Ⅶ TracesⅡ
　2 Integral formulas
　3 The trace in the induced representation
　4 The trace in the discrete series
　5 Relation between the Harish transforms on A and K
　Appendix. General facts about traces
Shapter Ⅷ The Planeherel Formula
　1 Calculus lemma
　2 The Harish transforms discontinuities
　3 Some lemmas
　4 The Plancherel formula
Chapter Ⅸ Discrete Series
　1 Discrete series in L2(G)
　2 Representation in the upper half plane
　3 Representation on the disc
　4 The lifting of weight m
　5 The holomorpbic property
Chapter Ⅹ Partial Differential Operators
　1 The universal enveloping algebra
　2 Analytic vectors
　3 Eigenfunctions of (f)
……