Download or read book A Construction of Singular Unitary Representations of Reductive Lie Groups written by Pierluigi Möseneder Frajria and published by . This book was released on 1988 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Unitary Representations of Reductive Lie Groups AM 118 Volume 118 written by David A. Vogan Jr. and published by Princeton University Press. This book was released on 2016-03-02 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.
Download or read book Unitary Representations of Reductive Lie Groups written by David A. Vogan and published by . This book was released on 1987 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.
Download or read book Representations of Real Reductive Lie Groups written by David A. Vogan and published by Birkhäuser. This book was released on 2016-06-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the foundations of infinite-dimensional representations of real reductive Lie groups. There are three major topics. First is the Langlands classification of irreducible representations. This is done using a generalization of parabolic induction due to Zuckerman. Second is the analysis of reducibility in certain standard families of representations. Third is the formulation of Kazhdan and Lusztig's conjectural character formulas for arbitrary irreducible representations. Since the first edition was published in 1981, the Kazhdan-Lusztig conjectures have been proved, and Zuckerman's construction has been connected to unitary representations. This second edition summarizes those developments and other progress in the field.
Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Download or read book Singular Unitary Representations and Discrete Series for Indefinite Stiefel Manifolds U p q F U p m q F written by Toshiyuki Kobayashi and published by American Mathematical Soc.. This book was released on 1992-01-01 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work treats a relatively singular part of the unitary dual of pseudo-orthogonal groups U(p,q;F) over F = R, C and H. These representations arise from discrete series for indefinite Stiefel manifolds U(p,q;F)/U(p - m,q,F)(2m 4p). Thanks to the duality theorem between d-module construction and Zuckerman's derived functor modules (ZDF-modules), these discrete series are naturally described in terms of ZF-modules with possibly singular parameters. The author's approach is algebraic and covers some parameters wandering outside the canonical Weyl chamber.
Download or read book Singular Unitary Representations and Discrete Series for Indefinite Stiefel Manifolds U p q mathbb F U p m q mathbb F written by Toshiyuki Kobayashi and published by American Mathematical Soc.. This book was released on 1992 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir examines the basic problem of finding vanishing theorems for Harish-Chandra modules. The results of these difficult problems contribute in a meaningful way to the singular unitary representation theory of reductive groups.
Download or read book Unitary Representation Theory for Solvable Lie Groups written by Jonathan Paul Brezin and published by American Mathematical Soc.. This book was released on 1968 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operator Algebras and Group Representations written by Grigore Arsene and published by Pitman Advanced Publishing Program. This book was released on 1984 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applications of Group Theory in Physics and Mathematical Physics written by Mosh Flato and published by American Mathematical Soc.. This book was released on 1985-12-31 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past decade has seen a renewal in the close ties between mathematics and physics. The Chicago Summer Seminar on Applications of Group Theory in Physics and Mathematical Physics, held in July, 1982, was organized to bring together a broad spectrum of scientists from theoretical physics, mathematical physics, and various branches of pure and applied mathematics in order to promote interaction and an exchange of ideas and results in areas of common interest. This volume contains the papers submitted by speakers at the Seminar. The reader will find several groups of articles varying from the most abstract aspects of mathematics to a concrete phenomenological description of some models applicable to particle physics. The papers have been divided into four categories corresponding to the principal topics covered at the Seminar. This is only a rough division, and some papers overlap two or more of these categories.
Download or read book Non Spherical Principal Series Representations of a Semisimple Lie Group written by Alfred Magnus and published by American Mathematical Soc.. This book was released on 1979 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-spherical principal series representations of a real semisimple Lie group are studied. These are representations, induced by a one-dimensional representation of a minimal parabolic subgroup, which have a one-dimensional subspace left stable by a maximal compact subgroup of the original group G. Necessary and sufficient conditions for such a representation to be irreducible, or to be cyclic, are found, in terms of parameters determined by certain rank one subgroups of G. A sufficient condition for such a representation to be unitary is found, and the condition is shown to be necessary in the rank one case.
Download or read book Kahler Spaces Nilpotent Orbits and Singular Reduction written by Johannes Huebschmann and published by American Mathematical Soc.. This book was released on 2004 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a stratified symplectic space, a suitable concept of stratified Kahler polarization encapsulates Kahler polarizations on the strata and the behaviour of the polarizations across the strata and leads to the notion of stratified Kahler space which establishes an intimate relationship between nilpotent orbits, singular reduction, invariant theory, reductive dual pairs, Jordan triple systems, symmetric domains, and pre-homogeneous spaces: The closure of a holomorphic nilpotent orbit or, equivalently, the closure of the stratum of the associated pre-homogeneous space of parabolic type carries a (positive) normal Kahler structure. In the world of singular Poisson geometry, the closures of principal holomorphic nilpotent orbits, positive definite hermitian JTS's, and certain pre-homogeneous spaces appear as different incarnations of the same structure. The closure of the principal holomorphic nilpotent orbit arises from a semisimple holomorphic orbit by contraction. Symplectic reduction carries a positive Kahler manifold to a positive normal Kahler space in such a way that the sheaf of germs of polarized functions coincides with the ordinary sheaf of germs of holomorphic functions. Symplectic reduction establishes a close relationship between singular reduced spaces and nilpotent orbits of the dual groups. Projectivization of holomorphic nilpotent orbits yields exotic (positive) stratified Kahler structures on complex projective spaces and on certain complex projective varieties including complex projective quadrics. The space of (in general twisted) representations of the fundamental group of a closed surface in a compact Lie group or, equivalently, a moduli space of central Yang-Mills connections on a principal bundle over a surface, inherits a (positive) normal (stratified) Kahler structure. Physical examples are provided by certain reduced spaces arising from angular momentum zero.
Download or read book Lie Group Representations III written by R. Herb and published by Springer. This book was released on 2006-11-14 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Analysis and Integral Geometry written by Eric Todd Quinto and published by American Mathematical Soc.. This book was released on 2013 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an historical overview of several decades in integral geometry and geometric analysis as well as recent advances in these fields and closely related areas. It contains several articles focusing on the mathematical work of Sigurdur Helgason, including an overview of his research by Gestur Olafsson and Robert Stanton.
Download or read book Lie Theory written by Jean-Philippe Anker and published by Springer Science & Business Media. This book was released on 2006-02-25 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Focuses on two fundamental questions related to semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications, and branching laws for unitary representations * Wide applications of compactification techniques * Concrete examples and relevant exercises engage the reader * Knowledge of basic representation theory of Lie groups, semisimple Lie groups and symmetric spaces is required
Download or read book Operator Algebras and Group Representations written by Institul national pentru creatie Stiintifica si tehnica and published by Pitman Advanced Publishing Program. This book was released on 1984 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Unitary Representations of Real Reductive Groups written by Jeffrey Adams and published by . This book was released on 2020 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
