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Books, Free Shipping, Sl2 R

Posted at: Offers to Sell and Export | Posted on: Tue 27 Jul, 2010 8:06 am | Product Category: Reference books [3760]
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Product Details

Author Serge Lang

Publisher World Publishing Corporation

Isbn 9787510004544, 7510004543


August 2009

Pages 428

Size 24k

Edition First

Format Paperback

Language English

Page material gelatine plate paper

Product Description:

Starting with Bargmann's 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.



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)


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