Vector Bundles and Representation Theory

Vector Bundles and Representation Theory PDF

Author: Steven Dale Cutkosky

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 258

ISBN-13: 0821832646

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This volume contains 13 papers from the conference on ``Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory''. The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field. Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the $S1$ fixed points in Quot-schemes and mirror principle computations for Grassmanians by S.-T. Yau, et al. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.

Representations of Elementary Abelian p-Groups and Vector Bundles

Representations of Elementary Abelian p-Groups and Vector Bundles PDF

Author: David J. Benson

Publisher: Cambridge University Press

Published: 2016-11-17

Total Pages:

ISBN-13: 1316802736

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Questions about modular representation theory of finite groups can often be reduced to elementary abelian subgroups. This is the first book to offer a detailed study of the representation theory of elementary abelian groups, bringing together information from many papers and journals, as well as unpublished research. Special attention is given to recent work on modules of constant Jordan type, and the methods involve producing and examining vector bundles on projective space and their Chern classes. Extensive background material is provided, which will help the reader to understand vector bundles and their Chern classes from an algebraic point of view, and to apply this to modular representation theory of elementary abelian groups. The final section, addressing problems and directions for future research, will also help to stimulate further developments in the subject. With no similar books on the market, this will be an invaluable resource for graduate students and researchers working in representation theory.

Singularities, Representation of Algebras, and Vector Bundles

Singularities, Representation of Algebras, and Vector Bundles PDF

Author: Gert-Martin Greuel

Publisher: Springer

Published: 2006-11-15

Total Pages: 396

ISBN-13: 3540478515

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It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers.

Basic Bundle Theory and K-Cohomology Invariants

Basic Bundle Theory and K-Cohomology Invariants PDF

Author: Dale Husemöller

Publisher: Springer

Published: 2007-12-10

Total Pages: 344

ISBN-13: 354074956X

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Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory. It aims to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, comes from quantum field theory, where topological invariants play an important role.

Vector Bundles and Their Applications

Vector Bundles and Their Applications PDF

Author: Glenys Luke

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 259

ISBN-13: 1475769237

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The book is devoted to the basic notions of vector bundles and their applications. The focus of attention is towards explaining the most important notions and geometric constructions connected with the theory of vector bundles. Theorems are not always formulated in maximal generality but rather in such a way that the geometric nature of the objects comes to the fore. Whenever possible examples are given to illustrate the role of vector bundles. Audience: With numerous illustrations and applications to various problems in mathematics and the sciences, the book will be of interest to a range of graduate students from pure and applied mathematics.

Moduli Spaces and Vector Bundles

Moduli Spaces and Vector Bundles PDF

Author: Steve Bradlow

Publisher: Cambridge University Press

Published: 2009-05-21

Total Pages: 516

ISBN-13: 0521734711

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Coverage includes foundational material as well as current research, authored by top specialists within their fields.

Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines

Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines PDF

Author: Hagen Meltzer

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 154

ISBN-13: 082183519X

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Deals with weighted projective lines, a class of non-commutative curves modelled by Geigle and Lenzing on a graded commutative sheaf theory. They play an important role in representation theory of finite-dimensional algebras; the complexity of the classification of coherent sheaves largely depends on the genus of these curves.

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