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Crystal Bases
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Book Synopsis Crystal Bases: Representations And Combinatorics by : Daniel Bump
Download or read book Crystal Bases: Representations And Combinatorics written by Daniel Bump and published by World Scientific Publishing Company. This book was released on 2017-01-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. This book approaches the subject directly from combinatorics, building crystals through local axioms (based on ideas by Stembridge) and virtual crystals. It also emphasizes parallels between the representation theory of the symmetric and general linear groups and phenomena in combinatorics. The combinatorial approach is linked to representation theory through the analysis of Demazure crystals. The relationship of crystals to tropical geometry is also explained.
Book Synopsis Introduction to Quantum Groups and Crystal Bases by : Jin Hong
Download or read book Introduction to Quantum Groups and Crystal Bases written by Jin Hong and published by American Mathematical Soc.. This book was released on 2002 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide an elementary introduction to the theory of quantum groups and crystal bases, focusing on the combinatorial aspects of the theory.
Download or read book Crystal Bases written by Daniel Bump and published by World Scientific Publishing Company. This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. This book approaches the subject directly from combinatorics, building crystals through local axioms (based on the ideas by Stembridge) and virtual crystals. It also emphasizes parallels between the representation theory of the symmetric and general linear group, and phenomena in combinatorics. The authors are both contributors to Sage, an open-source mathematical software system, which has strong support for crystal bases and combinatorics and the book takes advantage of this.
Book Synopsis Representations of Groups by : Bruce Normansell Allison
Download or read book Representations of Groups written by Bruce Normansell Allison and published by American Mathematical Soc.. This book was released on 1995 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representations of Groups contains papers presented at the Canadian Mathematical Society Annual Seminar held in June 1994, in Banff, Alberta, Canada.
Book Synopsis Recent Developments in Quantum Affine Algebras and Related Topics by : Naihuan Jing
Download or read book Recent Developments in Quantum Affine Algebras and Related Topics written by Naihuan Jing and published by American Mathematical Soc.. This book was released on 1999 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying "centre stage" in the theory of infinite dimensional Lie theory.
Book Synopsis Proceedings of the Third International Algebra Conference by : Yuen Fong
Download or read book Proceedings of the Third International Algebra Conference written by Yuen Fong and published by Springer Science & Business Media. This book was released on 2003-07-31 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new proceedings is a collection of papers presenting the recent developments and research in various fields of algebra, especially Lie Algebras, Rings and their related topics undertaken in the U.S.A., Russia, North Asia and Israel. Contributors include E. Zelmanov, the 1994 Fields Medalist, L. Bokut, Günter F. Pilz, Koichiro Harada, Alexander Kemer, V.K. Kharchenko, L. Makar-Limanov and Louis H. Rowen.
Book Synopsis Algebras, Representations and Applications by : V. Futorny
Download or read book Algebras, Representations and Applications written by V. Futorny and published by American Mathematical Soc.. This book was released on 2009 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions from the conference on "Algebras, Representations and Applications" (Maresias, Brazil, August 26-September 1, 2007), in honor of Ivan Shestakov's 60th birthday. The collection of papers presented here is of great interest to graduate students and researchers working in the theory of Lie and Jordan algebras and superalgebras and their representations, Hopf algebras, Poisson algebras, Quantum Groups, Group Rings and other topics.
Book Synopsis Technical Abstract Bulletin by : Defense Documentation Center (U.S.)
Download or read book Technical Abstract Bulletin written by Defense Documentation Center (U.S.) and published by . This book was released on 1961-04 with total page 1746 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Representations of Lie Algebras, Quantum Groups and Related Topics by : Naihuan Jing
Download or read book Representations of Lie Algebras, Quantum Groups and Related Topics written by Naihuan Jing and published by American Mathematical Soc.. This book was released on 2018-08-21 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12–13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac–Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever–Novikov algebras, representations of quantum groups, and related topics.
Book Synopsis Highlights in Lie Algebraic Methods by : Anthony Joseph
Download or read book Highlights in Lie Algebraic Methods written by Anthony Joseph and published by Springer Science & Business Media. This book was released on 2011-10-20 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of expository and research articles that highlight the various Lie algebraic methods used in mathematical research today. Key topics discussed include spherical varieties, Littelmann Paths and Kac–Moody Lie algebras, modular representations, primitive ideals, representation theory of Artin algebras and quivers, Kac–Moody superalgebras, categories of Harish–Chandra modules, cohomological methods, and cluster algebras.
Book Synopsis Studies in Lie Theory by : Joseph Bernstein
Download or read book Studies in Lie Theory written by Joseph Bernstein and published by Springer Science & Business Media. This book was released on 2006-07-27 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains new results on different aspects of Lie theory, including Lie superalgebras, quantum groups, crystal bases, representations of reductive groups in finite characteristic, and the geometric Langlands program
Book Synopsis MathPhys Odyssey 2001 by : Masaki Kashiwara
Download or read book MathPhys Odyssey 2001 written by Masaki Kashiwara and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'MathPhys Odyssey 2001' will serve as an excellent reference text for mathematical physicists and graduate students in a number of areas.; Kashiwara/Miwa have a good track record with both SV and Birkhauser.
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Tensor Categories by : Pavel Etingof
Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Download or read book Ramanujan 125 written by Ae Ja Yee, and published by American Mathematical Soc.. This book was released on 2014-10-14 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of an international conference to commemorate the 125th anniversary of Ramanujan's birth, held from November 5-7, 2012, at the University of Florida, Gainesville, Florida. Srinivasa Ramanujan was India's most famous mathematician. This volume contains research and survey papers describing recent and current developments in the areas of mathematics influenced by Ramanujan. The topics covered include modular forms, mock theta functions and harmonic Maass forms, continued fractions, partition inequalities, -series, representations of affine Lie algebras and partition identities, highly composite numbers, analytic number theory and quadratic forms.
Download or read book Boot and Shoe Recorder written by and published by . This book was released on 1918 with total page 978 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applications of Crystal Bases to Current Problems in Representation Theory by : Philip Max Sternberg
Download or read book Applications of Crystal Bases to Current Problems in Representation Theory written by Philip Max Sternberg and published by . This book was released on 2006 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
