Hilbert Schemes Of Points And Infinite Dimensional Lie Algebras
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Hilbert Schemes Of Points And Infinite Dimensional Lie Algebras
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Author : Zhenbo Qin
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-02-26
Hilbert Schemes Of Points And Infinite Dimensional Lie Algebras written by Zhenbo Qin 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 2018-02-26 with Hilbert schemes categories.
Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes of collections of points (zero-dimensional subschemes) in a smooth algebraic surface . Schemes turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of , including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of and the Gromov–Witten correspondence. The last part of the book presents results about quantum cohomology of and related questions. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, combinatorics, topology, number theory, and theoretical physics.
Infinite Dimensional Aspects Of Representation Theory And Applications
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Author : Stephen Berman
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Infinite Dimensional Aspects Of Representation Theory And Applications written by Stephen Berman 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 2005 with Mathematics categories.
The University of Virginia (Charlottesville) hosted an international conference on Infinite-dimensional Aspects of Representation Theory and Applications. This volume contains papers resulting from the mini-courses and talks given at the meeting. Beyond the techniques and ideas related to representation theory, the book demonstrates connections to number theory, algebraic geometry, and mathematical physics. The specific topics covered include Hecke algebras, quantum groups, infinite-dimensional Lie algebras, quivers, modular representations, and Gromov-Witten invariants. The book is suitable for graduate students and researchers interested in representation theory.
Lectures On Hilbert Schemes Of Points On Surfaces
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Author : Hiraku Nakajima
language : en
Publisher: American Mathematical Soc.
Release Date :
Lectures On Hilbert Schemes Of Points On Surfaces written by Hiraku Nakajima 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 with Mathematics categories.
The Hilbert scheme $X{[n] $ of a surface $X$ describes collections of $n$ (not necessarily distinct) points on $X$. More precisely, it is the moduli space for $0$-dimensional subschemes of $X$ of length $n$. Recently it was realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory-even theoretical physics. The discussion in the book reflects this feature of Hilbert schemes. For example, a construction of the representation of the infinite dimensional Heisenberg algebra (i.e., Fock space) is presented. This representation has been studied extensively in the literature in connection with affine Lie algebras, conformal field theory, etc. However, the construction presented in this volume is completely unique and provides the unexplored link between geometry and representation theory. The book offers a nice survey of current developments in this rapidly growing subject. It is suitable as a text at the advanced graduate level.
Infinite Dimensional Lie Algebras
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Author : Victor G. Kac
language : en
Publisher: Cambridge University Press
Release Date : 1990
Infinite Dimensional Lie Algebras written by Victor G. Kac and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
The third, substantially revised edition of a monograph concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie albegras, and their representations, based on courses given over a number of years at MIT and in Paris.
Recent Developments In Infinite Dimensional Lie Algebras And Conformal Field Theory
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Author : Stephen Berman
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Recent Developments In Infinite Dimensional Lie Algebras And Conformal Field Theory written by Stephen Berman 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 2002 with Mathematics categories.
Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, ``Infinite-Dimensional Lie Theory and Conformal Field Theory'', held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field. Thisconference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual interest. The talks focused on recent developments in the representation theory of affine, quantum affine, and extended affine Lie algebras and Lie superalgebras. They also highlightedapplications to conformal field theory, integrable and disordered systems. Some of the articles are expository and accessible to a broad readership of mathematicians and physicists interested in this area; others are research articles that are appropriate for more advanced readers.
Infinite Dimensional Lie Algebras
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Author : Victor G. Kac
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09
Infinite Dimensional Lie Algebras written by Victor G. Kac 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 2013-11-09 with Mathematics categories.
Cohomology Of Infinite Dimensional Lie Algebras
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Author : D.B. Fuks
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Cohomology Of Infinite Dimensional Lie Algebras written by D.B. Fuks 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.
There is no question that the cohomology of infinite dimensional Lie algebras deserves a brief and separate mono graph. This subject is not cover~d by any of the tradition al branches of mathematics and is characterized by relative ly elementary proofs and varied application. Moreover, the subject matter is widely scattered in various research papers or exists only in verbal form. The theory of infinite-dimensional Lie algebras differs markedly from the theory of finite-dimensional Lie algebras in that the latter possesses powerful classification theo rems, which usually allow one to "recognize" any finite dimensional Lie algebra (over the field of complex or real numbers), i.e., find it in some list. There are classifica tion theorems in the theory of infinite-dimensional Lie al gebras as well, but they are encumbered by strong restric tions of a technical character. These theorems are useful mainly because they yield a considerable supply of interest ing examples. We begin with a list of such examples, and further direct our main efforts to their study.
Lie Algebras
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Author : Gerard G. A. Bäuerle
language : en
Publisher: North Holland
Release Date : 1990
Lie Algebras written by Gerard G. A. Bäuerle and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Finite element method categories.
This is the long awaited follow-up to Lie Algebras, Part I which covered a major part of the theory of Kac-Moody algebras, stressing primarily their mathematical structure. Part II deals mainly with the representations and applications of Lie Algebras and contains many cross references to Part I. The theoretical part largely deals with the representation theory of Lie algebras with a triangular decomposition, of which Kac-Moody algebras and the Virasoro algebra are prime examples. After setting up the general framework of highest weight representations, the book continues to treat topics as the Casimir operator and the Weyl-Kac character formula, which are specific for Kac-Moody algebras. The applications have a wide range. First, the book contains an exposition on the role of finite-dimensional semisimple Lie algebras and their representations in the standard and grand unified models of elementary particle physics. A second application is in the realm of soliton equations and their infinite-dimensional symmetry groups and algebras. The book concludes with a chapter on conformal field theory and the importance of the Virasoro and Kac-Moody algebras therein.
Lectures On Hilbert Schemes Of Points On Surfaces
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Author : Hiraku Nakajima
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Lectures On Hilbert Schemes Of Points On Surfaces written by Hiraku Nakajima 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.
It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.
Analytic Number Theory Approximation Theory And Special Functions
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Author : Gradimir V. Milovanović
language : en
Publisher: Springer
Release Date : 2014-07-08
Analytic Number Theory Approximation Theory And Special Functions written by Gradimir V. Milovanović and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Mathematics categories.
This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.