A proof of Wahl's conjecture in the symplectic case

Abstract

Let X denote a flag variety of type A or type C. We construct a canonical Frobenius splitting of X × X which vanishes with maximal multiplicty along the diagonal. This way we verify a conjecture by Lakshmibai, Mehta and Parameswaran [4] in type C, and obtain a new proof in type A. In particular, we obtain a proof of Wahl's conjecture in type C, and a new proof in type A. We also present certain cohomological consequences.

Spherical varieties and Wahl’s conjecture

“…This conjecture has been considered by several authors (see for example [15], [12], [5], [13], [18]). In particular Brown and Lakshmibai in [5] proved this conjecture for minuscule homogeneous varieties using Representation Theoretic techniques and a case by case analysis.…”