Multidimensional Hypergeometric Functions The Representation Theory Of Lie Algebras And Quantum Groups PDF Download
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Author | : Alexander Varchenko |
Publisher | : World Scientific |
Total Pages | : 383 |
Release | : 1995-03-29 |
Genre | : Mathematics |
ISBN | : 981450162X |
Download Multidimensional Hypergeometric Functions The Representation Theory Of Lie Algebras And Quantum Groups Book in PDF, ePub and Kindle
This book recounts the connections between multidimensional hypergeometric functions and representation theory. In 1984, physicists Knizhnik and Zamolodchikov discovered a fundamental differential equation describing correlation functions in conformal field theory. The equation is defined in terms of a Lie algebra. Kohno and Drinfeld found that the monodromy of the differential equation is described in terms of the quantum group associated with the Lie algebra. It turns out that this phenomenon is the tip of the iceberg. The Knizhnik-Zamolodchikov differential equation is solved in multidimensional hypergeometric functions, and the hypergeometric functions yield the connection between the representation theories of Lie algebras and quantum groups. The topics presented in this book are not adequately covered in periodicals.
Author | : Aleksandr Nikolaevich Varchenko |
Publisher | : World Scientific Publishing Company Incorporated |
Total Pages | : 371 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 9789810218805 |
Download Multidimensional Hypergeometric Functions and Representation Theory of Lie Algebras and Quantum Groups Book in PDF, ePub and Kindle
This book recounts the connections between multidimensional hypergeometric functions and representation theory. In 1984, physicists Knizhnik and Zamolodchikov discovered a fundamental differential equation describing correlation functions in conformal field theory. The equation is defined in terms of a Lie algebra. Kohno and Drinfeld found that the monodromy of the differential equation is described in terms of the quantum group associated with the Lie algebra. It turns out that this phenomenon is the tip of the iceberg. The Knizhnik-Zamolodchikov differential equation is solved in multidimensional hypergeometric functions, and the hypergeometric functions yield the connection between the representation theories of Lie algebras and quantum groups. The topics presented in this book are not adequately covered in periodicals.
Author | : Bangming Deng |
Publisher | : American Mathematical Soc. |
Total Pages | : 790 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821841866 |
Download Finite Dimensional Algebras and Quantum Groups Book in PDF, ePub and Kindle
"The interplay between finite dimensional algebras and Lie theory dates back many years. In more recent times, these interrelations have become even more strikingly apparent. This text combines, for the first time in book form, the theories of finite dimensional algebras and quantum groups. More precisely, it investigates the Ringel-Hall algebra realization for the positive part of a quantum enveloping algebra associated with a symmetrizable Cartan matrix and it looks closely at the Beilinson-Lusztig-MacPherson realization for the entire quantum $\mathfrak{gl}_n$. The book begins with the two realizations of generalized Cartan matrices, namely, the graph realization and the root datum realization. From there, it develops the representation theory of quivers with automorphisms and the theory of quantum enveloping algebras associated with Kac-Moody Lie algebras. These two independent theories eventually meet in Part 4, under the umbrella of Ringel-Hall algebras. Cartan matrices can also be used to define an important class of groups--Coxeter groups--and their associated Hecke algebras. Hecke algebras associated with symmetric groups give rise to an interesting class of quasi-hereditary algebras, the quantum Schur algebras. The structure of these finite dimensional algebras is used in Part 5 to build the entire quantum $\mathfrak{gl}_n$ through a completion process of a limit algebra (the Beilinson-Lusztig-MacPherson algebra). The book is suitable for advanced graduate students. Each chapter concludes with a series of exercises, ranging from the routine to sketches of proofs of recent results from the current literature."--Publisher's website.
Author | : Aleksandr Nikolaevich Varchenko |
Publisher | : American Mathematical Soc. |
Total Pages | : 130 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821828673 |
Download Special Functions, KZ Type Equations, and Representation Theory Book in PDF, ePub and Kindle
The last twenty years have seen an active interaction between mathematics and physics. This book is devoted to one of the new areas which deals with mathematical structures related to conformal field theory and its sqs-deformations. In the book, the author discusses the interplay between Knizhnik-Zamolodchikov type equations, the Bethe ansatz method, representation theory, and geometry of multi-dimensional hypergeometric functions. This book aims to provide an introduction to the area and expose different facets of the subject. It contains constructions, discussions of notions, statements of main results, and illustrative examples. The exposition is restricted to the simplest case of the theory associated with the Lie algebra s\mathfrak{sl 2s. This book is intended for researchers and graduate students in mathematics and in mathematical physics, in particular to those interested in applications of special functions.
Author | : K. Behrend |
Publisher | : Springer |
Total Pages | : 325 |
Release | : 2004-10-12 |
Genre | : Mathematics |
ISBN | : 3540456171 |
Download Quantum Cohomology Book in PDF, ePub and Kindle
The book gathers the lectures given at the C.I.M.E. summer school "Quantum Cohomology" held in Cetraro (Italy) from June 30th to July 8th, 1997. The lectures and the subsequent updating cover a large spectrum of the subject on the field, from the algebro-geometric point of view, to the symplectic approach, including recent developments of string-branes theories and q-hypergeometric functions.
Author | : Niky Kamran |
Publisher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : 1994-01-01 |
Genre | : Mathematics |
ISBN | : 9780821854945 |
Download Lie Algebras, Cohomology, and New Applications to Quantum Mechanics, Book in PDF, ePub and Kindle
This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrodinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a "hidden" symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.
Author | : Alexander Astashkevich |
Publisher | : American Mathematical Soc. |
Total Pages | : 362 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 9780821820322 |
Download Differential Topology, Infinite-Dimensional Lie Algebras, and Applications Book in PDF, ePub and Kindle
This volume presents contributions by leading experts in the field. The articles are dedicated to D.B. Fuchs on the occasion of his 60th birthday. Contributors to the book were directly influenced by Professor Fuchs, and include his students, friends, and professional colleagues. In addition to their research, they offer personal reminicences about Professor Fuchs, giving insight into the history of Russian mathematics.
Author | : Naihuan Jing |
Publisher | : American Mathematical Soc. |
Total Pages | : 233 |
Release | : 2018-08-21 |
Genre | : Algebra |
ISBN | : 1470436965 |
Download Representations of Lie Algebras, Quantum Groups and Related Topics Book in PDF, ePub and Kindle
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.
Author | : Victor G. Kac |
Publisher | : World Scientific |
Total Pages | : 250 |
Release | : 2013 |
Genre | : Mathematics |
ISBN | : 9814522201 |
Download Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras Book in PDF, ePub and Kindle
The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras--such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations--simplify and clarify the constructions of the first edition of the book. -- Cover.
Author | : Erik Koelink |
Publisher | : American Mathematical Soc. |
Total Pages | : 362 |
Release | : 2022-08-30 |
Genre | : Education |
ISBN | : 1470465205 |
Download Hypergeometry, Integrability and Lie Theory Book in PDF, ePub and Kindle
This volume contains the proceedings of the virtual conference on Hypergeometry, Integrability and Lie Theory, held from December 7–11, 2020, which was dedicated to the 50th birthday of Jasper Stokman. The papers represent recent developments in the areas of representation theory, quantum integrable systems and special functions of hypergeometric type.