On the Cohomology of Theta Divisors of Hyperelliptic Jacobians
  We prove that k-th singular cohomology group of the complement of the theta divisor in a hyperelliptic Jacobian is isomorphic to the k-th fundamental representation of the symplectic group Sp(2g,C). This is one of the conjectures in our previous paper. 
Atsushi Nakayashiki