Representation Theory of Lie Groups [First Edition] 0-8218-1941-0, 9780821819418

Table of contents :
Content: A. W. Knapp and P. E. Trapa, Representations of semisimple Lie groups: Introduction Some representations of $SL(n, \mathbb{R})$ Semsimple groups and structure theory Introduction to representation theory Cartan subalgebras and highest weights Action by the Lie algebra Cartan subgroups and global characters Discrete series and asymptotics Langlands classification Bibliography R. Zierau, Representations in Dolbeault cohomology: Introduction Complex flag varieties and orbits under a real form Open $G_0$-orbits Examples, homogeneous bundles Dolbeault cohomology, Bott-Borel-Weil theorem Indefinite harmonic theory Intertwining operators I Intertwining operators II The linear cycle space Bibliography L. Barchini, Unitary representations attached to elliptic orbits. A geometric approach: Introduction Globalizations Dolbeault cohomology and maximal globalization $L^2$-cohomology and discrete series representations Indefinite quantization Bibliography D. A. Vogan, Jr., The method of adjoint orbits for real reductive groups: Introduction Some ideas from mathematical physics The Jordan decomposition and three kinds of quantization Complex polarizations The Kostant-Sekiguchi correspondence Quantizing the action of $K$ Associated graded modules A good basis for associated graded modules Proving unitarity Exercises Bibliography K. Vilonen, Geometric methods in representation theory: Introduction Overview Derived categories of constructible sheaves Equivariant derived categories Functors to representations Matsuki correspondence for sheaves Characteristic cyles The character formula Microlocalization of Matsuki = Sekiguchi Homological algebra (appendix by M. Hunziker) Bibliography Jian-Shu Li, Minimal representations and reductive dual pairs: Introduction The oscillator representation Models Duality Classification Unitarity Minimal representations of classical groups Dual pairs in simple groups Bibliography.

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