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Dirac Operators in Representation Theory
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by
Jing-Song Huang, Pavle Pandzic
This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Dirac operators are widely used in physics, differential geometry, and group-theoretic settings (particularly, the geometric construction of discrete series representations). The related concept of Dirac cohomology, which is defined ...
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Groups and Representations
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J. L. Alperin
The aim of this text is to provide a concise treatment of some topics from group theory and representation theory for a one term course. It focuses on the non-commutative side of the field emphasizing the general linear group as the most important group and example. The book should enable graduate students from every mathematical field, as well as ...
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The symmetric group representations, combinatorial algorithms, and symmetric functions
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by
Sagan
This text is an introduction to the representation theory of the symmetric group from three different points of view: via general representation theory, via combinatorial algorithms, and via symmetric functions. It is the only book to deal with all three aspects of this subject at once. The style of presentation is relaxed yet rigorous and the ...
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Finite Reductive Groups, Related Structures and Representations
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Marc Cabanes (Editor)
This volume focuses on the representation theory of groups and related structures, combining the modular representation theory of finite groups of Richard Brauer and the representation theory of reductive groups of George Lusztig.
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Automorphic Representation of Unitary Groups in Three Variables. (Am-123)
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by
Jonathan D Rogawski
The subject matter of these Notes is the interplay between the theory of automorphic forms and group representations. One goal is to interpret some recent developments in this area, most significantly the theory of Jacquet-Langlands, working out, whenever possible, explicit consequences and connections with the classical theory. Another goal is to ...
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Representation theory of finite groups and associative algebras
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Charles W Curtis
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Representations Modulaires Des Groupes Reductifs P-Adiques. Representations Cuspidales de Gl(n)
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Marie France Vigneras
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Automorphic Representations of Unitary Groups in Three Variables
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Jonathan D Rogawski
The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many ...
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Studies in Memory of Issai Schur
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Anthony Joseph (Editor), Anna Melnikov, Rudolf Rentschler (Editor)
This volume is dedicated to the memory of Issai Schur. It opens with some biographical reminiscences of the famous school he established in Berlin, his brutal dismissal by the Nazi regime and his tragic end in Palestine. This is followed by an extensive review of the extraordinary impact of his lesser known analytic work. Finally, leading ...
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The Langlands Classification and Irreducible Characters for Reductive Groups
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Jeffrey Adams, D a Vogan (Editor), D Barbasch (Editor)
This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the Weil-Deligne group. For p-adic fields, this conjecture has not been proved; but it has been refined to a ...
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The Orbit Method in Representation PM'82
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by
Dulfo, Pederson, Vergne
Ever since its introduction around 1960 by Kirillov, the orbit method has played a major role in representation theory of Lie groups and Lie algebras. This book contains the proceedings of a conference held from August 29 to September 2, 1988, at the University of Copenhagen, about 'the orbit method in representation theory'. It contains ten ...
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Representations and Characters of Groups
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by
G D James
This book provides a modern introduction to the representation theory of finite groups. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. The character tables of many groups are given, including all groups of order less than 32, and all ...
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Schur Algebras and Representation Theory
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by
Stuart Martin
The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups (both finite and infinite). In the text Dr Martin gives a full, self-contained account of this algebra and these links, covering both the basic theory of Schur algebras and related areas. He discusses the usual ...
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Principles of Symmetry, Dynamics, and Spectroscopy
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by
William G. Harter
Designed for physicists and chemists who desire a deeper understanding of symmetry principles as they are applied to atomic and molecular dynamics and spectroscopy, this volume examines theoretical techniques while developing the mathematics in a logical and straightforward manner.
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Explicit Brauer Induction
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by
Victor P Snaith, Bela Bollobas (Editor), W Fulton (Editor)
Explicit Brauer Induction is a new and important technique in algebra, discovered by the author in 1986. It solves an old problem, giving a canonical formula for Brauer's induction theorem. In this book it is derived algebraically, following a method of R. Boltje - thereby making the technique, previously topological, accessible to algebraists. ...
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Linear Representations of Finite Groups
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Jean-Pierre Serre
This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. This is a fundamental result of constant use in mathematics as well as in quantum chemistry or physics. The examples ...
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Unitary Representations of Reductive Lie Groups
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by
David A Vogan, Jr.
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 ...
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Introduction to Lie Algebras and Representation Theory
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by
James E Humphreys
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 ...
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Noncommutative Distributions: Unitary Representation of Gauge Groups and Algebras
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by
Sergio Albeverio, Raphael J Hoegh-Krohn, Jean A Marion
Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras. Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary ...
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Linear representations of groups
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by
E B Vinberg (Editor)
This textbook contains a comprehensive and detailed exposition of the fundamentals of the representation theory of groups, especially of finite groups and compact groups. The exposition is based on the decomposition of the two-sided regular representation. This enables the author to give not only an abstract description of the representations but ...
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An introduction to harmonic analysis on semisimple Lie groups
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by
Varadarajan
Now in paperback, this graduate-level textbook is an introduction to the representation theory of semi-simple Lie groups. As such, it will be suitable for research students in algebra and analysis, and for research mathematicians requiring a readable account of the topic. The author emphasizes the development of the central themes of the subject ...
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Geometry and Representation Theory of Real and P-Adic Lie Groups
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by
Juan Tirao (Editor), David A Vogan, Jr. (Editor), Joe Wolf (Editor)
This text provides a thorough introduction to the more active parts of representation theory and to some of its ongoing applications.
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Linearity, Symmetry, and Prediction in the Hydrogen Atom
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by
Stephanie F Singer
The predictive power of mathematics in quantum phenomena is one of the great intellectual successes of the 20th century. This textbook, aimed at undergraduate or graduate level students (depending on the college or university), concentrates on how to make predictions about the numbers of each kind of basic state of a quantum system from only two ...
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Similarity Problems and Completely Bounded Maps
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by
Gilles Pisier
These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* -algebras and the third one with the disc algebra. We describe them in detail in the ...
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The Admissible Dual of Gl(n) Via Compact Open Subgroups
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Colin J Bushnell
This work gives a full description of a method for analyzing the admissible complex representations of the general linear group G = Gl(N,F) of a non-Archimedean local field F in terms of the structure of these representations when they are restricted to certain compact open subgroups of G. The authors define a family of representations of these ...
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