Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-07-07
Physics
High Energy Physics
High Energy Physics - Theory
37 pages, LaTeX2e. wrong statement in subsection 4.2 corrected and rest of the paper adapted
Scientific paper
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.
Fuchs J"urgen
Schweigert Christoph
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