Download or read book Regular Quasi regular and Induced Representations of Infinite dimensional Groups written by Alexander V. Kosyak and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The aim of the book is a systematic development, by example, of noncommutative harmonic analysis on infinite-dimensional (non-locally compact) matrix groups. We generalize the notion of regular, quasi-regular and induced representations for arbitrary infinite-dimensional groups. The central idea to verify the irreducibility is the Ismagilov conjecture. We also extend the Kirillov orbit method for the group of upper triangular matrices of infinite order." - publisher

Download or read book Induced Representations of Infinite dimensional Groups I written by Alexander V. Kosyak and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Automorphic Representations of Low Rank Groups written by Yuval Zvi Flicker and published by World Scientific. This book was released on 2006 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called ?liftings?. This book concentrates on two initial examples: the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of PGL(2) in SL(3); and basechange from the unitary group U(3, E/F) to GL(3, E), [E: F] = 2.The book develops the technique of comparison of twisted and stabilized trace formulae and considers the ?Fundamental Lemma? on orbital integrals of spherical functions. Comparison of trace formulae is simplified using ?regular? functions and the ?lifting? is stated and proved by means of character relations.This permits an intrinsic definition of partition of the automorphic representations of SL(2) into packets, and a definition of packets for U(3), a proof of multiplicity one theorem and rigidity theorem for SL(2) and for U(3), a determination of the self-contragredient representations of PGL(3) and those on GL(3, E) fixed by transpose-inverse-bar. In particular, the multiplicity one theorem is new and recent.There are applications to construction of Galois representations by explicit decomposition of the cohomology of Shimura varieties of U(3) using Deligne's (proven) conjecture on the fixed point formula.

Download or read book The Theory of Group Representations written by George Whitelaw Mackey and published by . This book was released on 1955 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

Download or read book Unitary Representations of Groups Duals and Characters written by Bachir Bekka and published by American Mathematical Soc.. This book was released on 2020-11-16 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unitary representations of groups play an important role in many subjects, including number theory, geometry, probability theory, partial differential equations, and quantum mechanics. This monograph focuses on dual spaces associated to a group, which are spaces of building blocks of general unitary representations. Special attention is paid to discrete groups for which the unitary dual, the most common dual space, has proven to be not useful in general and for which other duals spaces have to be considered, such as the primitive dual, the normal quasi-dual, or spaces of characters. The book offers a detailed exposition of these alternative dual spaces and covers the basic facts about unitary representations and operator algebras needed for their study. Complete and elementary proofs are provided for most of the fundamental results that up to now have been accessible only in original papers and appear here for the first time in textbook form. A special feature of this monograph is that the theory is systematically illustrated by a family of examples of discrete groups for which the various dual spaces are discussed in great detail: infinite dihedral group, Heisenberg groups, affine groups of fields, solvable Baumslag-Solitar group, lamplighter group, and general and special linear groups. The book will appeal to graduate students who wish to learn the basics facts of an important topic and provides a useful resource for researchers from a variety of areas. The only prerequisites are a basic background in group theory, measure theory, and operator algebras.

Download or read book Fundamentals of Infinite Dimensional Representation Theory written by Raymond C. Fabec and published by CRC Press. This book was released on 2018-10-03 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject. From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.

Download or read book Modern Theory of Dynamical Systems written by Anatole Katok and published by American Mathematical Soc.. This book was released on 2017-06-19 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tribute to one of the founders of modern theory of dynamical systems, the late Dmitry Victorovich Anosov. It contains both original papers and surveys, written by some distinguished experts in dynamics, which are related to important themes of Anosov's work, as well as broadly interpreted further crucial developments in the theory of dynamical systems that followed Anosov's original work. Also included is an article by A. Katok that presents Anosov's scientific biography and a picture of the early development of hyperbolicity theory in its various incarnations, complete and partial, uniform and nonuniform.

Download or read book Quasiregular Representations of the Infinite Dimensional Nilpotent Group written by Sergio Albeverio and published by . This book was released on 2006 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Download or read book Quasiregular Representations of the Infinite Dimensional Borelian Group written by Sergio Albeverio and published by . This book was released on 2003 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Representations of Finite Dimensional Algebras written by Hiroyuki Tachikawa and published by American Mathematical Soc.. This book was released on 1991 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Tsukuba International Conference on Representations of Algebras and Related Topics (fifth ICRA), held at the University of Tsukuba, August 13-18, 1990. The conference focused on the rapid development of research on representations of finite-dimensional algebras and group representations. A subset of the fifty-seven lectures are collected here, together with a number of other papers not originally presented at the conference. With contributions by some of the world's leading experts in this area, this book provides a valuable overview of the frontier of research in representations of algebras.

Download or read book Infinite Dimensional Representations of 2 Groups written by John C. Baez and published by American Mathematical Soc.. This book was released on 2012 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Just as groups can have representations on vector spaces, 2-groups have representations on 2-vector spaces, but Lie 2-groups typically have few representations on the finite-dimensional 2-vector spaces introduced by Kapranov and Voevodsky. Therefore, Crane, Sheppeard, and Yetter introduced certain infinite-dimensional 2-vector spaces, called measurable categories, to study infinite-dimensional representations of certain Lie 2-groups, and German and North American mathematicians continue that work here. After introductory matters, they cover representations of 2-groups, and measurable categories, representations on measurable categories. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).

Download or read book Renormalization Singular Currents and Representations of Infinite Dimensional Groups on Quantized Fields written by Jan Pedersen and published by . This book was released on 1991 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fundamentals of Infinite Dimensional Representation Theory written by Raymond C. Fabec and published by . This book was released on 2000 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Representations of the Infinite Symmetric Group written by Alexei Borodin and published by Cambridge University Press. This book was released on 2017 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.

Download or read book Elements of the Theory of Representations written by A. A. Kirillov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of a master mathematician. He has the duty of retaining as far as possible the flavor and spirit of the original, at the same time rendering it into a readable and idiomatic form of the language into which the translation is made. All of this is challenging. At the same time, the translator should never forget that he is not a creator, but only a mirror. His own viewpoints, his own preferences, should never lead him into altering the original, even with the best intentions. Only an occasional translator's note is permitted. The undersigned is grateful for the opportunity of translating Professor Kirillov's fine book on group representations, and hopes that it will bring to the English-reading mathematical public as much instruction and interest as it has brought to the translator. Deviations from the Russian text have been rigorously avoided, except for a number of corrections kindly supplied by Professor Kirillov. Misprints and an occasional solecism have been tacitly taken care of. The trans lation is in all essential respects faithful to the original Russian. The translator records his gratitude to Linda Sax, who typed the entire translation, to Laura Larsson, who prepared the bibliography (considerably modified from the original), and to Betty Underhill, who rendered essential assistance.