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The strange duality conjecture for generic curves

Author(s): Prakash Belkale
Journal: J. Amer. Math. Soc. 21 (2008), 235-258.
MSC (2000): Primary 14H60; Secondary 14D20
Posted: 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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Additional Information:

Prakash Belkale
Affiliation: Department of Mathematics, University of North Carolina-Chapel Hill, CB \#3250, Phillips Hall, Chapel Hill, North Carolina 27599
Email: belkale@email.unc.edu

DOI: 10.1090/S0894-0347-07-00569-3
PII: S 0894-0347(07)00569-3
Received by editor(s): February 23, 2006
Posted: April 25, 2007
Additional Notes: The author was partially supported by NSF grant DMS-0300356.
Copyright of article: Copyright 2007, American Mathematical Society

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A. Marian and D. Oprea, The level-rank duality for non-abelian theta functions , Inventiones Mathematicae Volume 168, Number 2 (2007), 23. MR 2289865

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