Mathematical Research Letters

Volume 21 (2014)

Number 6

Strange duality revisited

Pages: 1353 – 1366



Christian Pauly (Laboratoire de Mathématiques J. A. Dieudonné, Université de Nice – Sophia Antipolis, Nice, France)


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

Published 2 April 2015