The rank-level duality for non-abelian theta functions

Abstract

We prove that the strange duality conjecture of Beauville-Donagi-Tu holds for all curves. We establish first a more extended rank-level duality, interesting in its own right, from which the standard rank-level duality follows by restriction.

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• Rank-one sheaves and stable pairs on surfaces
• GV-sheaves, Fourier-Mukai transform, and Generic Vanishing
• Coset Vertex Operator Algebras and $\W$-Algebras
• A weighted topological quantum field theory for Quot schemes on curves
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• Moduli spaces of 1-dimensional semi-stable sheaves and Strange duality on ${\mathbb{P}}^2$
• Moduli of objects in finite length abelian categories
• Representations in Strange Duality: Hilbert Schemes paired with higher rank spaces
• Some examples of vector bundles in the base locus of the generalized theta divisor
• Strange Duality of Verlinde spaces for G_2 and F_4