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Developments and Retrospectives in Lie Theory

Part of the Developments in Mathematics Book Series (volume 37)

Editors: Mason, Geoffrey; Penkov, Ivan; Wolf, Joseph A.

DOI: 10.1007/978-3-319-09934-7

ISBN: 978-3-319-09933-0

Publisher: Springer International Publishing - Springer Journals

Oct 15, 2014

1 - 9 of 9 Chapters

LitStream

Chapter 1Group Gradings on Lie Algebras and Applications to Geometry: II

Bahturin, Yuri; Goze, Michel; Remm, Elisabeth

Pages: 1 –40

[This paper is devoted to some applications of the theory of group gradings on Lie algebras to two topics of differential geometry, such as generalized symmetric manifolds and affine structures on nilmanifolds.]
LitStream

Chapter 2Harmonic Analysis on Homogeneous Complex Bounded Domains and Noncommutative Geometry

Bieliavsky, Pierre; Gayral, Victor; de Goursac, Axel; Spinnler, Florian

Pages: 41 –76

[We define and study a noncommutative Fourier transform on every homogeneous complex bounded domain. We then give an application in noncommutative differential geometry by defining noncommutative Baumslag–Solitar tori.]
LitStream

Chapter 3The Radon Transform and Its Dual for Limits of Symmetric Spaces

Hilgert, Joachim; Ólafsson, Gestur

Pages: 77 –111

[The Radon transform and its dual are central objects in geometric analysis on Riemannian symmetric spaces of the noncompact type. In this article we study algebraic versions of those transforms on inductive limits of symmetric spaces. In particular, we show that normalized versions exists on...
LitStream

Chapter 4Cycle Connectivity and Automorphism Groups of Flag Domains

Huckleberry, Alan

Pages: 113 –126

[A flag domain D is an open orbit of a real form G0 in a flag manifold Z=G∕P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 5Shintani Functions, Real Spherical Manifolds, and Symmetry Breaking Operators

Kobayashi, Toshiyuki

Pages: 127 –159

[For a pair of reductive groups G ⊃ G′, we prove a geometric criterion for the space Sh(λ, ν) of Shintani functions to be finite-dimensional in the Archimedean case. This criterion leads us to a complete classification of the symmetric pairs (G, G′) having finite-dimensional Shintani spaces. A...
LitStream

Chapter 6Harmonic Spinors on Reductive Homogeneous Spaces

Mehdi, Salah; Zierau, Roger

Pages: 161 –181

[An integral intertwining operator is given from certain principal series representations into spaces of harmonic spinors for Kostant’s cubic Dirac operator. This provides an integral representation for harmonic spinors on a large family of reductive homogeneous spaces.]
LitStream

Chapter 7Twisted Harish–Chandra Sheaves and Whittaker Modules: The Nondegenerate Case

Miličić, Dragan; Soergel, Wolfgang

Pages: 183 –196

[In this paper we develop a geometric approach to the study of the category of Whittaker modules. As an application, we reprove a well-known result of B. Kostant on the structure of the category of nondegenerate Whittaker modules.]
LitStream

Chapter 8Unitary Representations of Unitary Groups

Neeb, Karl-Hermann

Pages: 197 –243

[In this paper we review and streamline some results of Kirillov, Olshanski and Pickrell on unitary representations of the unitary group U(ℋ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
LitStream

Chapter 9Weak Splittings of Quotients of Drinfeld and Heisenberg Doubles

Yakimov, Milen

Pages: 245 –268

[We investigate the fine structure of the symplectic foliations of Poisson homogeneous spaces. Two general results are proved for weak splittings of surjective Poisson submersions from Heisenberg and Drinfeld doubles. The implications of these results are that the torus orbits of symplectic...

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