Quantum Linear Groups PDF Download
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Author | : Brian Parshall |
Publisher | : American Mathematical Soc. |
Total Pages | : 168 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : 0821825011 |
Download Quantum Linear Groups Book in PDF, ePub and Kindle
We consider the theory of quantum groups as a natural abstraction of the theory of affine group schemes. After establishing the foundational results as the theory of induced representations, rational cohomology, and the Hochschild-Serre spectral sequence, we take up a detailed investigation of the quantum linear group [italic]GL[italic subscript]q([italic]n). In particular, we develop the global and infinitesimal representation theory of [italic]GL[italic subscript]q([italic]n) and its subgroups.
Author | : Jonathan Brundan |
Publisher | : American Mathematical Soc. |
Total Pages | : 127 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821826166 |
Download Quantum Linear Groups and Representations of $GL_n({\mathbb F}_q)$ Book in PDF, ePub and Kindle
We give a self-contained account of the results originating in the work of James and the second author in the 1980s relating the representation theory of GL[n(F[q) over fields of characteristic coprime to q to the representation theory of "quantum GL[n" at roots of unity. The new treatment allows us to extend the theory in several directions. First, we prove a precise functorial connection between the operations of tensor product in quantum GL[n and Harish-Chandra induction in finite GL[n. This allows us to obtain a version of the recent Morita theorem of Cline, Parshall and Scott valid in addition for p-singular classes. From that we obtain simplified treatments of various basic known facts, such as the computation of decomposition numbers and blocks of GL[n(F[q) from knowledge of the same for the quantum group, and the non-defining analogue of Steinberg's tensor product theorem. We also easily obtain a new double centralizer property between GL[n(F[[q) and quantum GL[n, generalizing a result of Takeuchi. Finally, we apply the theory to study the affine general linear group, following ideas of Zelevinsky in characteristic zero. We prove results that can be regarded as the modular analogues of Zelevinsky's and Thoma's branching rules. Using these, we obtain a new dimension formula for the irreducible cross-characteristic representations of GL[n(F[q), expressing their dimensions in terms of the characters of irreducible modules over the quantum group.
Author | : Pavel I. Etingof |
Publisher | : |
Total Pages | : 242 |
Release | : 2010 |
Genre | : Mathematical physics |
ISBN | : 9781571462077 |
Download Lectures on Quantum Groups Book in PDF, ePub and Kindle
Author | : Ross Street |
Publisher | : Cambridge University Press |
Total Pages | : 160 |
Release | : 2007-01-18 |
Genre | : Mathematics |
ISBN | : 1139461443 |
Download Quantum Groups Book in PDF, ePub and Kindle
Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a 'coalgebra'. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term 'quantum group', along with revolutionary new examples, was launched by Drinfel'd in 1986.
Author | : Masud Chaichian |
Publisher | : World Scientific |
Total Pages | : 362 |
Release | : 1996 |
Genre | : Science |
ISBN | : 9789810226237 |
Download Introduction to Quantum Groups Book in PDF, ePub and Kindle
In the past decade there has been an extemely rapid growth in the interest and development of quantum group theory.This book provides students and researchers with a practical introduction to the principal ideas of quantum groups theory and its applications to quantum mechanical and modern field theory problems. It begins with a review of, and introduction to, the mathematical aspects of quantum deformation of classical groups, Lie algebras and related objects (algebras of functions on spaces, differential and integral calculi). In the subsequent chapters the richness of mathematical structure and power of the quantum deformation methods and non-commutative geometry is illustrated on the different examples starting from the simplest quantum mechanical system — harmonic oscillator and ending with actual problems of modern field theory, such as the attempts to construct lattice-like regularization consistent with space-time Poincaré symmetry and to incorporate Higgs fields in the general geometrical frame of gauge theories. Graduate students and researchers studying the problems of quantum field theory, particle physics and mathematical aspects of quantum symmetries will find the book of interest.
Author | : Jie Du |
Publisher | : |
Total Pages | : 13 |
Release | : 1992 |
Genre | : Linear algebraic groups |
ISBN | : 9780646123134 |
Download IC Bases and Quantum Linear Groups Book in PDF, ePub and Kindle
Author | : Hermann Weyl |
Publisher | : Courier Corporation |
Total Pages | : 468 |
Release | : 1950-01-01 |
Genre | : Mathematics |
ISBN | : 9780486602691 |
Download The Theory of Groups and Quantum Mechanics Book in PDF, ePub and Kindle
This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.
Author | : Ka Chun Tse |
Publisher | : |
Total Pages | : 72 |
Release | : 2001 |
Genre | : Linear algebraic groups |
ISBN | : |
Download Representations of General Linear Groups and Quantum Groups Book in PDF, ePub and Kindle
Author | : Anatoli Klimyk |
Publisher | : Springer Science & Business Media |
Total Pages | : 568 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3642608965 |
Download Quantum Groups and Their Representations Book in PDF, ePub and Kindle
This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.
Author | : Jean Pierre Serre |
Publisher | : |
Total Pages | : 170 |
Release | : 1996 |
Genre | : |
ISBN | : |
Download Linear Representations of Finite Groups Book in PDF, ePub and Kindle