Strange duality revisited

We give a proof of the strange duality or rank-level duality of the WZW models of conformal blocks by extending the genus-$0$ result, obtained by Nakanishi–Tsuchiya in 1992, to higher genus curves via the sewing procedure. The new ingredient of the proof is an explicit use of the branching rules of the conformal embedding of affine Lie algebras $\widehat{\mathfrak{sl}(r)} \times \widehat{\mathfrak{sl}(l)} \subset \widehat{\mathfrak{sl}(rl)}$. We recover the strange duality of spaces of generalized theta functions obtained by Belkale, Marian–Oprea, as well as by Oudompheng in the parabolic case.

2010 Mathematics Subject Classification

14D20, 14H60, 17B67, 81T40

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Published 2 April 2015