A representation theoretic approach to the WZW Verlinde formula

Abstract

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.

arXiv comment37 pages, LaTeX2e. wrong statement in subsection 4.2 corrected and rest of the paper adapted

References in corpus (9)

• A matrix S for all simple current extensions
• Derivation of the Verlinde Formula from Chern-Simons Theory and the G/G model
• Conformal blocks, fusion rules and the Verlinde formula
• Vector bundles on curves and generalized theta functions: recent results and open problems
• The resolution of field identification fixed points in diagonal coset theories
• On algebraic equations satisfied by hypergeometric correlators in WZW models. II
• Fusion, Crossing and Monodromy in Conformal Field Theory Based on $SL(2)$ Current Algebra with Fractional Level
• $A_1^{(1)}$ Admissible Representations -- Fusion Transformations and Local Correlators
• General branching functions of affine Lie algebras

Cited by in corpus (2)

• Topologizations of Chiral Representations
• On Moduli of G-bundles over Curves for exceptional G