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:
Acceso en línea:http://cds.cern.ch/record/329645
Descripción
Sumario: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.