A representation theoretic approach to the WZW Verlinde formula

By exploring the description of chiral blocks in terms of co-invariants, a proof of the Verlinde formula for WZW models is obtained which is entirely based on the representation theory of affine Lie algebras. In contrast to other proofs of the Verlinde formula, this approach works for all untwisted...

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Detalles Bibliográficos
Autores principales: Fuchs, Jurgen, Schweigert, Christoph
Lenguaje:eng
Publicado: 1997
Materias:
Particle Physics - Theory
Acceso en línea:http://cds.cern.ch/record/329645
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author Fuchs, Jurgen
Schweigert, Christoph
author_facet Fuchs, Jurgen
Schweigert, Christoph
author_sort Fuchs, Jurgen
collection CERN
description By exploring the description of chiral blocks in terms of co-invariants, a proof of the Verlinde formula for WZW models is obtained which is entirely based on the representation theory of affine Lie algebras. In contrast to other proofs of the Verlinde formula, this approach works for all untwisted affine Lie algebras. As a by-product we obtain a homological interpretation of the Verlinde multiplicities, as Euler characteristics of complexes built from invariant tensors of finite-dimensional simple Lie algebras.
id cern-329645
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1997
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spelling cern-3296452023-03-12T05:49:49Zhttp://cds.cern.ch/record/329645engFuchs, JurgenSchweigert, ChristophA representation theoretic approach to the WZW Verlinde formulaParticle Physics - TheoryBy exploring the description of chiral blocks in terms of co-invariants, a proof of the Verlinde formula for WZW models is obtained which is entirely based on the representation theory of affine Lie algebras. In contrast to other proofs of the Verlinde formula, this approach works for all untwisted affine Lie algebras. As a by-product we obtain a homological interpretation of the Verlinde multiplicities, as Euler characteristics of complexes built from invariant tensors of finite-dimensional simple Lie algebras.By exploring the description of chiral blocks in terms of co-invariants, a derivation of the Verlinde formula for WZW models is obtained which is entirely based on the representation theory of affine Lie algebras. In contrast to existing proofs of the Verlinde formula, this approach works universally for all untwisted affine Lie algebras. As a by-product we obtain a homological interpretation of the Verlinde multiplicities as Euler characteristics of complexes built from invariant tensors of finite-dimensional simple Lie algebras. Our results can also be used to compute certain traces of automorphisms on the spaces of chiral blocks. Our argument is not rigorous; in its present form this paper will therefore not be submitted for publication.hep-th/9707069CERN-TH-97-152CERN-TH-97-152oai:cds.cern.ch:3296451997-07-08
spellingShingle Particle Physics - Theory
Fuchs, Jurgen
Schweigert, Christoph
A representation theoretic approach to the WZW Verlinde formula
title A representation theoretic approach to the WZW Verlinde formula
title_full A representation theoretic approach to the WZW Verlinde formula
title_fullStr A representation theoretic approach to the WZW Verlinde formula
title_full_unstemmed A representation theoretic approach to the WZW Verlinde formula
title_short A representation theoretic approach to the WZW Verlinde formula
title_sort representation theoretic approach to the wzw verlinde formula
topic Particle Physics - Theory
url http://cds.cern.ch/record/329645
work_keys_str_mv AT fuchsjurgen arepresentationtheoreticapproachtothewzwverlindeformula
AT schweigertchristoph arepresentationtheoreticapproachtothewzwverlindeformula
AT fuchsjurgen representationtheoreticapproachtothewzwverlindeformula
AT schweigertchristoph representationtheoreticapproachtothewzwverlindeformula

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