Starting with Bargmann's paPer on the tnhmte dimenslonal representattons of SL2(R),the theory of representations of semisimple Lie groups has evolved toa rather extensive production.
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书名 | SL2(R) |
分类 | 科学技术-自然科学-数学 |
作者 | (美)莱恩 |
出版社 | 世界图书出版公司 |
下载 | ![]() |
简介 | 编辑推荐 Starting with Bargmann's paPer on the tnhmte dimenslonal representattons of SL2(R),the theory of representations of semisimple Lie groups has evolved toa rather extensive production. 目录 Notation Chapter Ⅰ General Results 1 The representation on Cv(G) 2 A criterion for complete reducibility 3 L2 kernels and operators 4 Plancherel measures Chapter Ⅱ Compact Groups 1 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 1 Integral formulas 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 Traces 1 Operators of trace class 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 Chapter Ⅷ The Planeherel Formula 1 Calculus lemma 2 The Harish transforms discontinuities 3 Some iemmas 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 holomorphic property Chapter Ⅹ Partial Differential Operators 1 The universal enveloping algebra 2 Analytic vectors 3 Eiaenfunctions of Z (f) Chapter Ⅺ The Well Representation 1 Some convolutions 2 Generators and relations for SL2 3 The Well representation Chapter Ⅻ Representation on OL2(Г\\G) 1 Cusps on the group 2 Cusp forms 3 A criterion for compact operators 4 Complete reducibility of OL2Г\\G) Chapter ⅩⅢ The Continuous Part of L2(Г\\G) 1 An orthogonality relation 2 The Eisenstein series 3 Analytic continuation and functional equation 4 Mellin and zeta transforms 5 Some group theoretic lemmas 6 An expression for TOTφ 7 Analytic continuation of the zeta transform of TOTφ 8 The spectral decomposition Chapter ⅩⅣ Spectral Decomposition of the Laplace Operator on Г\\■ 1 Geometry and differential operators on ■ 2 A solution of ιφ≠s(ι-s)φ 3 The resoivant of the Laplace operator on ■ for σ>I 4 Symmetry of the Laplace operator on Г\\■ 5 The Laplace operator on Г\\■ 6 Green's functions and the Whittaker equation 7 Decomposition of the resolvant on Г\\■ for o>3/2 8 The equation - ψ″(y)=s(ι-s)/y2ψ(y) on [α, ∞) 9 Eigenfunctions of the Laplace, an in L2(Г\\■)=H 10 The resolvant equations for 0 <α<2 11 The kernel of the resolvant for 0 <α< 2 12 The Eisenstein operator and Eisenstein functions 13 The continuous part of the spectrum 14 Several cusps 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 PDE 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 Bibliography Symbols Frequently Used Index |
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