Multidimensional Hypergeometric Functions And Representation Theory Of Lie Algebras And Quantum Groups

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Multidimensional Hypergeometric Functions The Representation Theory Of Lie Algebras And Quantum Groups

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Author : Alexander Varchenko
language : en
Publisher: World Scientific
Release Date : 1995-03-29

Multidimensional Hypergeometric Functions The Representation Theory Of Lie Algebras And Quantum Groups written by Alexander Varchenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-29 with Mathematics categories.

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.

Multidimensional Hypergeometric Functions And Representation Theory Of Lie Algebras And Quantum Groups

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Author : Aleksandr Nikolaevich Varchenko
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1995

Multidimensional Hypergeometric Functions And Representation Theory Of Lie Algebras And Quantum Groups written by Aleksandr Nikolaevich Varchenko and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

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.

Special Functions Kz Type Equations And Representation Theory

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Author : Aleksandr Nikolaevich Varchenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Special Functions Kz Type Equations And Representation Theory written by Aleksandr Nikolaevich Varchenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

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.

Quantum Cohomology

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Author : K. Behrend
language : en
Publisher: Springer
Release Date : 2004-10-12

Quantum Cohomology written by K. Behrend and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-12 with Mathematics categories.

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.

Differential Topology Infinite Dimensional Lie Algebras And Applications

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Author : Alexander Astashkevich
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Differential Topology Infinite Dimensional Lie Algebras And Applications written by Alexander Astashkevich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

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. The main topics addressed in this unique work are infinite-dimensional Lie algebras with applications (vertex operator algebras, conformal field theory, quantum integrable systems, etc.) and differential topology. The volume provides an excellent introduction to current research in the field.

Representations Of Lie Algebras Quantum Groups And Related Topics

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Author : Naihuan Jing
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-21

Representations Of Lie Algebras Quantum Groups And Related Topics written by Naihuan Jing and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-21 with Mathematics categories.

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.

Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras

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Author : Victor G. Kac
language : en
Publisher: World Scientific
Release Date : 2013

Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras written by Victor G. Kac and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.

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.

Two Dimensional Conformal Geometry And Vertex Operator Algebras

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Author : Yi-Zhi Huang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Two Dimensional Conformal Geometry And Vertex Operator Algebras written by Yi-Zhi Huang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc- tures of conformal field theories. Much of the recent progress has deep connec- tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac- Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on.He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a big and important problem. On the one hand, the theory of vertex operator algebras and their repre- sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.

Low Dimensional Topology And Number Theory

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Author : Masanori Morishita
language : en
Publisher: Springer Nature
Release Date : 2025-03-02

Low Dimensional Topology And Number Theory written by Masanori Morishita and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-02 with Mathematics categories.

This book is the result of research initiatives formed during the workshop "Low Dimensional Topology and Number Theory XIII" at Kyushu University in 2022. It is also dedicated to the memory of Professor Toshie Takata, who has been a main figure of the session chairs for the series of annual workshops since 2009. The activity was aimed at understanding and deepening recent developments of lively and fruitful interactions between low-dimensional topology and number theory over the past decades. In this volume of proceedings, the reader will find research papers as well as survey articles, including open problems, at the interface between classical and quantum topology, and algebraic and analytic number theory, written by leading experts and active researchers in the respective fields. Topics include, among others, the strong slope conjecture; Kashiwara–Vergne Lie algebra; braids and fibered double branched covers of 3-manifolds; Temperley–Lieb–Jones category andconformal blocks; WRT invariants and false theta functions; the colored Jones polynomial of the figure-eight knot; potential functions and A-polynomials; l-adic Galois polylogarithms; Dijkgraaf–Witten invariants in Bloch groups; analogies between knots and primes in arithmetic topology; normalized Jones polynomials for rational links; Iwasawa main conjecture; Weber’s class number problem. The book provides a valuable resource for researchers and graduate students interested in topics related to both low-dimensional topology and number theory.

Encyclopaedia Of Mathematics

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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.