The strange duality conjecture for generic curves

Belkale, Prakash

doi:10.1090/S0894-0347-07-00569-3

The strange duality conjecture for generic curves
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by Prakash Belkale

J. Amer. Math. Soc. 21 (2008), 235-258

DOI: https://doi.org/10.1090/S0894-0347-07-00569-3

Published electronically: April 25, 2007

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Abstract:

Let $X$ be a smooth connected projective algebraic curve of genus $g\geq 1$. The strange duality conjecture connects non-abelian theta functions of rank $r$ and level $k$ and those of rank $k$ and level $r$ on $X$ (for $SU(r)$ and $\operatorname {U}(k)$, respectively). In this paper we prove this conjecture for $X$ generic in the moduli space of curves of genus $g$.

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