Author : Laurence Corwin
Publisher : Cambridge University Press
Page : 286 pages
File Size : 19,44 MB
Release : 1990-08-30
Category : Mathematics
ISBN : 9780521604956
The first exposition of group representations and harmonic analysis for graduates for over twenty years.
Author : Laurence Corwin
Publisher : Cambridge University Press
Page : 280 pages
File Size : 37,33 MB
Release : 2004-06-03
Category : Mathematics
ISBN : 9780521604956
There has been no exposition of group representations and harmonic analysis suitable for graduate students for over twenty years. In this, the first of two projected volumes, the authors remedy the situation by surveying all the basic theory developed since the pioneering work of Kirillov in 1958, and consolidating more recent results. Topics covered include basic Kirillov theory, algorithms for parametrizing all coadjoint orbits. The authors have not only given here a modern account of all topics necessary for current research, but have also included many computed examples. This volume can serve then either as a handbook for specialists, with a complete, self-contained exposition of major results, or as a textbook suitable for graduate courses in harmonic analysis.
Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 34,36 MB
Release : 2008-07-31
Category : Mathematics
ISBN : 0521889693
This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Author : Lawrence J. Corwin
Publisher :
Page : 500 pages
File Size : 50,50 MB
Release : 1990
Category :
ISBN :
Author : J.E. Humphreys
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 11,79 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461263980
This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.
Author : Robert Gilmore
Publisher : Cambridge University Press
Page : 5 pages
File Size : 43,16 MB
Release : 2008-01-17
Category : Science
ISBN : 113946907X
Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.
Author : Didier Arnal
Publisher : Cambridge University Press
Page : 463 pages
File Size : 11,38 MB
Release : 2020-04-16
Category : Mathematics
ISBN : 1108428096
A complete and self-contained account of the basic theory of unitary group representations for graduate students and researchers.
Author : Asim Orhan Barut
Publisher : World Scientific
Page : 750 pages
File Size : 44,41 MB
Release : 1986
Category : Mathematics
ISBN : 9789971502171
Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
Author : Victor G. Kac
Publisher : Springer
Page : 545 pages
File Size : 48,31 MB
Release : 2018-12-12
Category : Mathematics
ISBN : 3030021912
This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of θ-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre)
Author : Roger William Carter
Publisher : Cambridge University Press
Page : 662 pages
File Size : 18,68 MB
Release : 2005-10-27
Category : Mathematics
ISBN : 9780521851381
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
