[2] A duality for symmetric spaces with applications to group representations, Advances in Math. , 5 (1970), l—l 5 + . T. Hirai [1] The characters of some induced representations of semisimple Lie groups J. Math. Kyoto Univ. , 8 (1968), ...

(1982b) Group algebras of finite p-solvable groups with radicals of the fourth power zero, Proc. Roy. Soc. Edinb. 92A, 205-231. (1982c) A remark on blocks with dihedral defect groups in solvable groups, Math. Z. 179, 401–406.

Author: Gregory Karpilovsky

Publisher: Elsevier

ISBN: 9781483295107

Category: Mathematics

Page:

View: 886

This volume is divided into three parts. Part I provides the foundations of the theory of modular representations. Special attention is drawn to the Brauer-Swan theory and the theory of Brauer characters. A detailed investigation of quadratic, symplectic and symmetric modules is also provided. Part II is devoted entirely to the Green theory: vertices and sources, the Green correspondence, the Green ring, etc. In Part III, permutation modules are investigated with an emphasis on the study of p-permutation modules and Burnside rings. The material is developed with sufficient attention to detail so that it can easily be read by the novice, although its chief appeal will be to specialists. A number of the results presented in this volume have almost certainly never been published before.

Index abelian group 360 homogeneous 364 invariants of 364 metric 360 nonsingular 360 symplectic 360 absolute degree 637 absolutely simple module 296 algebra 320 definable over a subfield 320 enveloping 330 G-normal 588 graded 394 ...

Author:

Publisher: Elsevier

ISBN: 0080872913

Category: Mathematics

Page: 906

View: 464

This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups. The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theory for group algebras. The volume ends with a detailed investigation of the Schur index for ordinary representations. A prominant role is played in the discussion by Brauer groups together with cyclotomic algebras and cyclic algebras.

By 0.2.6, all free representations of varX are contained in VSCX = X. Since every representation from varX is an ... Since group representations are two-sorted algebraic structures, one should not be surprised when some statements on ...

Author: Samuel M. Vovsi

Publisher: Cambridge University Press

ISBN: 9780521424103

Category: Mathematics

Page: 200

View: 532

This book is devoted to the theory of group representations and is intended for a broad audience of researchers and graduate students.

Sherman, T., 1966, A Weight Theory for Unitary Representations, Canad. J. Math. 18, 159–168. Shiga, K., 1955, Representations of a Compact Group on a Banach Space, J. Math. Soc. Japan 7, 224–248. Shoda, K., 1933, Uber die monomialen ...

Author: A Barut

Publisher: World Scientific Publishing Company

ISBN: 9789813103870

Category: Mathematics

Page: 740

View: 778

The material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book on group representations, neither in mathematical nor in physical literature and it is hoped that this book will prove to be useful in many areas of research. It is highly recommended as a textbook for an advanced course in mathematical physics on Lie algebras, Lie groups and their representations. Request Inspection Copy

M. W. Baldoni-Silva and H. Kraljevic, "Composition factors of the principal series representations of the group Sp (n, l) ", Trans. Amer. Math. Soc. 262 (1980), 447–471. 4. V. Bargmann, "Irreducible unitary representations of the ...

CHAPTER 3 GROUP REPRESENTATIONS In geometrical and physical applications, group theory is closely associated with symmetry transformations of the systems under study. In classical physics, the interest lies in the effect of the symmetry ...

Author: Wu-Ki Tung

Publisher: World Scientific Publishing Company

ISBN: 9789813104044

Category: Representations of groups

Page: 336

View: 188

An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet. Request Inspection Copy

COWLING Unitary and uniformly bounded representations of some simple Lie groups . ... DUFLO Construction de représentations unitaires d'un groupe de Lie HOWE On a notion of rank for unitary representations of the classical groups .

Author: A. Figà Talamanca

Publisher: Springer Science & Business Media

ISBN: 9783642111174

Category: Mathematics

Page: 476

View: 925

Lectures: A. Auslander, R. Tolimeri: Nilpotent groups and abelian varieties.- M Cowling: Unitary and uniformly bounded representations of some simple Lie groups.- M. Duflo: Construction de representations unitaires d’un groupe de Lie.- R. Howe: On a notion of rank for unitary representations of the classical groups.- V.S. Varadarajan: Eigenfunction expansions of semisimple Lie groups.- R. Zimmer: Ergodic theory, group representations and rigidity.- Seminars: A. Koranyi: Some applications of Gelfand pairs in classical analysis.

Introduction to Group Representations and Characters. Assume that No.(3 b >) Z N. Then Na(< b >) = Co(b)u, where u is an involution which inverts Ca(b). Put q = |Ca(b), q > 9. One easily verifies that Na(< b >)a, a £ Na(< b >), contains ...

Author:

Publisher: Elsevier

ISBN: 0080872867

Category: Mathematics

Page: 653

View: 356

Part A: Background Material and Part B: Introduction to Group Representations and Characters

His book [Ma4] contains a systematic exposition of an extensive part of quantum theory from the point of view of unitary group representations. In his later years he gave some detailed expositions of his approach to the group theoretic ...

Author: Robert S. Doran

Publisher: American Mathematical Soc.

ISBN: 9780821842256

Category: Mathematics

Page: 446

View: 953

George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics. Topics examined here include recent results on induced representations, virtual groups, the Mackey Machine and crossed products, representations of Baumslag-Solitar groups, the Radon transform and the heat equation, groupoids in the study of wavelets, and quantum theory. The in-depth historical surveys of Mackey's work on representation theory, ergodic theory, and physics, together with recent developments inspired by his fundamental work will be of considerable interest to both graduate students and researchers alike.