Elliptic Quantum Groups: Representations and Related Geometry, Konno Hitoshi
Автор: Watrous, John (university Of Waterloo, Ontario) Название: The theory of quantum information ISBN: 1107180562 ISBN-13(EAN): 9781107180567 Издательство: Cambridge Academ Рейтинг: Цена: 11563.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Intended for graduate students and researchers, this book presents a formal development of the mathematical theory of quantum information. Largely self-contained, with clear proofs and a wide range of exercises, it will help the reader grasp the fundamental facts and techniques that form the mathematical foundations of the subject.
Описание: This is the first book to study representations of elementary abelian groups using vector bundles on projective space. The treatment includes substantial background material from representation theory and algebraic geometry, including an algebraic treatment of the theory of Chern classes.
Автор: Vvedensky Dimitri D, Evans Timothy S Название: Symmetry, Groups, And Representations In Physics ISBN: 1786340151 ISBN-13(EAN): 9781786340153 Издательство: World Scientific Publishing Цена: 10138.00 р. Наличие на складе: Поставка под заказ.
Описание: This book is an introduction to symmetry in physics based on discrete and continuous groups. No knowledge of algebra is assumed and the book is suitable for both beginning and advanced graduate students. In fact, at Imperial College, the notes on which this book is based have been thoroughly tested in the classroom by two lecturers with quite different backgrounds (condensed matter theory and field theory) to classes composed of third- and fourth-year undergraduate students as well as students from the MSc in Quantum Fields and Fundamental Forces program. Abundant exercises, all with detailed solutions that are available in a separate instructor's manual, are included to illustrate the concepts introduced in the main text, to extend some of the main results, and to introduce new ideas. One of the main themes in the book is the application of group theory to physical problems.
Описание: 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.
Автор: Bachir Bekka, Pierre de la Harpe Название: Unitary Representations of Groups, Duals, and Characters ISBN: 1470456273 ISBN-13(EAN): 9781470456276 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 19820.00 р. Наличие на складе: Нет в наличии.
Описание: Unitary representations of groups play an important role in many subjects, including number theory, geometry, probability theory, partial differential equations, and quantum mechanics. This book focuses on dual spaces associated to a group, which are spaces of building blocks of general unitary representations.
Автор: Snaith, Victor P (univ Of Sheffield, Uk) Название: Derived langlands: monomial resolutions of admissible representations ISBN: 981327574X ISBN-13(EAN): 9789813275744 Издательство: World Scientific Publishing Рейтинг: Цена: 19008.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The Langlands Programme is one of the most important areas in modern pure mathematics. The importance of this volume lies in its potential to recast many aspects of the programme in an entirely new context. For example, the morphisms in the monomial category of a locally p-adic Lie group have a distributional description, due to Bruhat in his thesis. Admissible representations in the programme are often treated via convolution algebras of distributions and representations of Hecke algebras. The monomial embedding, introduced in this book, elegantly fits together these two uses of distribution theory. The author follows up this application by giving the monomial category treatment of the Bernstein Centre, classified by Deligne-Bernstein-Zelevinsky.This book gives a new categorical setting in which to approach well-known topics. Therefore, the context used to explain examples is often the more generally accessible case of representations of finite general linear groups. For example, Galois base-change and epsilon factors for locally p-adic Lie groups are illustrated by the analogous Shintani descent and Kondo-Gauss sums, respectively. General linear groups of local fields are emphasized. However, since the philosophy of this book is essentially that of homotopy theory and algebraic topology, it includes a short appendix showing how the buildings of Bruhat-Tits, sufficient for the general linear group, may be generalised to the tom Dieck spaces (now known as the Baum-Connes spaces) when G is a locally p-adic Lie group.The purpose of this monograph is to describe a functorial embedding of the category of admissible k-representations of a locally profinite topological group G into the derived category of the additive category of the admissible k-monomial module category. Experts in the Langlands Programme may be interested to learn that when G is a locally p-adic Lie group, the monomial category is closely related to the category of topological modules over a sort of enlarged Hecke algebra with generators corresponding to characters on compact open modulo the centre subgroups of G. Having set up this functorial embedding, how the ingredients of the celebrated Langlands Programme adapt to the context of the derived monomial module category is examined. These include automorphic representations, epsilon factors and L-functions, modular forms, Weil-Deligne representations, Galois base change and Hecke operators.
Автор: Woit, Peter Название: Quantum theory, groups and representations ISBN: 3319878352 ISBN-13(EAN): 9783319878355 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject.
Автор: Hermann Weyl. Название: The Classical Groups: Their Invariants and Representations ISBN: 0691057567 ISBN-13(EAN): 9780691057569 Издательство: Wiley Рейтинг: Цена: 14573.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Discusses the symmetric, linear, orthogonal, and symplectic groups and determines their invariants and representations. This book covers topics such as matrix algebras, semigroups, commutators, and spinors, which help in understanding the group-theoretic structure of quantum mechanics.
Описание: A polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley-Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.
Описание: Canonical commutation relations (CCR) and canonical anti-commutation relations (CAR) are basic principles in quantum physics including both quantum mechanics with finite degrees of freedom and quantum field theory.
Описание: Aimed at advanced students and active researchers in mathematics or theoretical physics, this book provides a detailed exposition of automorphic forms and representations, from the basics up to cutting-edge research topics at the interface between number theory and string theory.
Автор: Anne-Marie Aubert; Manish Mishra; Alan Roche; Stev Название: Representations of Reductive p-adic Groups ISBN: 9811366276 ISBN-13(EAN): 9789811366277 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Поставка под заказ.
Описание: This book consists of survey articles and original research papers in the representation theory of reductive p-adic groups. In particular, it includes a survey by Anne-Marie Aubert on the enormously influential local Langlands conjectures. The survey gives a precise and accessible formulation of many aspects of the conjectures, highlighting recent refinements, due to the author and her collaborators, and their current status. It also features an extensive account by Colin Bushnell of his work with Henniart on the fine structure of the local Langlands correspondence for general linear groups, beginning with a clear overview of Bushnell–Kutzko’s construction of cuspidal types for such groups. The remaining papers touch on a range of topics in this active area of modern mathematics: group actions on root data, explicit character formulas, classification of discrete series representations, unicity of types, local converse theorems, completions of Hecke algebras, p-adic symmetric spaces. All meet a high level of exposition. The book should be a valuable resource to graduate students and experienced researchers alike.
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