Strange duality revisited

2012/04/05 by Christian Pauly, Pauly, Christian
Mathematics · #14D20 #14H60 #17B67 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14D20 #msc:14H60 #msc:17B67

paper · pdf · doi:10.48550/arxiv.1204.1186

10 pages

arxiv created 2012/04/05 · arxiv updated 2012/04/06

Abstract

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 the affine Lie algebras sl(r) x sl(l) in 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.

Related

• Rank-level duality of Conformal Blocks for odd orthogonal Lie algebras in genus 0
• Rank-level duality of conformal blocks of GL_n and SL_n
• Strange Duality of Verlinde spaces for G₂ and F₄
• Strange duality and the Hitchin/WZW connection
• Diagram automorphisms and Rank-Level duality