The strange duality conjecture for generic curves

Abstract

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