On The Structure Of Principal Subspaces Of Standard Modules For Affine Lie Algebras Of Type A
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Affine Vertex And W Algebras
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Author : Dražen Adamović
language : en
Publisher: Springer Nature
Release Date : 2019-11-28
Affine Vertex And W Algebras written by Dražen Adamović and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-28 with Mathematics categories.
This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory. It is widely accepted in the mathematical community that the best way to study the representation theory of affine Kac–Moody algebras is by investigating the representation theory of the associated affine vertex and W-algebras. In this volume, this general idea can be seen at work from several points of view. Most relevant state of the art topics are covered, including fusion, relationships with finite dimensional Lie theory, permutation orbifolds, higher Zhu algebras, connections with combinatorics, and mathematical physics. The volume is based on the INdAM Workshop Affine, Vertex and W-algebras, held in Rome from 11 to 15 December 2017. It will be of interest to all researchers in the field.
On The Structure Of Principal Subspaces Of Standard Modules For Affine Lie Algebras Of Type A
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Author : Christopher Michael Sadowski
language : en
Publisher:
Release Date : 2014
On The Structure Of Principal Subspaces Of Standard Modules For Affine Lie Algebras Of Type A written by Christopher Michael Sadowski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Lie algebras categories.
Using the theory of vertex operator algebras and intertwining operators, we obtain presentations for the principal subspaces of all the standard $widehat{goth{sl}(3)}$-modules. Certain of these presentations had been conjectured and used in work of Calinescu to construct exact sequences leading to the graded dimensions of certain principal subspaces. We prove the conjecture in its full generality for all standard $widehat{goth{sl}(3)}$-modules. We then provide a conjecture for the case of $widehat{goth{sl}(n)}$, $n ge 4$. In addition, we construct completions of certain universal enveloping algebras and provide a natural setting for families of defining relations for the principal subspaces of standard modules for untwisted affine Lie algebras. We also use the theory of vertex operator algebras and intertwining operators, along with conjecturally assumed presentations for certain principal subspaces, to construct exact sequences among principal subspaces of certain standard $widehat{mathfrak{sl}(n)}$-modules, $n ge 3$. As a consequence, we obtain the multigraded dimensions of the principal subspaces $W(k_1Lambda_1 + k_2 Lambda_2)$ and $W(k_{n-2}Lambda_{n-2} + k_{n-1} Lambda_{n-1})$. This generalizes earlier work by Calinescu on principal subspaces of standard $widehat{mathfrak{sl}(3)}$-modules, where similar assumptions were made.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2008
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Dissertation Abstracts International
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Author :
language : en
Publisher:
Release Date : 2007
Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Dissertations, Academic categories.
Science Citation Index
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Author :
language : en
Publisher:
Release Date : 1993
Science Citation Index written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.
Vols. for 1964- have guides and journal lists.
Structure Of The Level One Standard Modules For The Affine Lie Algebras B Subscript L 1 F4 1 And G2 1
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Author : Frank Rimlinger
language : en
Publisher:
Release Date : 1987
Structure Of The Level One Standard Modules For The Affine Lie Algebras B Subscript L 1 F4 1 And G2 1 written by Frank Rimlinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Clifford algebras categories.
Vertex Operator Algebras And Related Areas
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Author : M. J. Bergvelt
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-10-01
Vertex Operator Algebras And Related Areas written by M. J. Bergvelt 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 2009-10-01 with Mathematics categories.
Vertex operator algebras were introduced to mathematics in the work of Richard Borcherds, Igor Frenkel, James Lepowsky and Arne Meurman as a mathematically rigorous formulation of chiral algebras of two-dimensional conformal field theory. The aim was to use vertex operator algebras to explain and prove the remarkable Monstrous Moonshine conjectures in group theory. The theory of vertex operator algebras has now grown into a major research area in mathematics. These proceedings contain expository lectures and research papers presented during the international conference on Vertex Operator Algebras and Related Areas, held at Illinois State University in Normal, IL, from July 7 to July 11, 2008. The main aspects of this conference were connections and interactions of vertex operator algebras with the following areas: conformal field theories, quantum field theories, Hopf algebra, infinite dimensional Lie algebras, and modular forms. This book will be useful for researchers as well as for graduate students in mathematics and physics. Its purpose is not only to give an up-to-date overview of the fields covered by the conference but also to stimulate new directions and discoveries by experts in the areas.
Integral Bases For Affine Lie Algebras And Their Universal Enveloping Algebras
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Author : David Mitzman
language : en
Publisher: American Mathematical Soc.
Release Date : 1985
Integral Bases For Affine Lie Algebras And Their Universal Enveloping Algebras written by David Mitzman 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 1985 with Mathematics categories.
A revised version of the author's PhD thesis written under the supervision of J Lepowsky at Rutgers University in 1983.
Studies In Modules Over Affine Lie Algebras
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Author : Jacob Greenstein
language : en
Publisher:
Release Date : 2001
Studies In Modules Over Affine Lie Algebras written by Jacob Greenstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
Inner Ideals And Geometries In Representations Of Affine Lie Algebras
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Author : Meighan Irene Dillon
language : en
Publisher:
Release Date : 1987
Inner Ideals And Geometries In Representations Of Affine Lie Algebras written by Meighan Irene Dillon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Geometry, Affine categories.