Symplectic restriction varieties and geometric branching rules II

In this paper, we introduce combinatorially defined subvarieties of symplectic flag varieties called symplectic restriction varieties. We study their geometric properties and compute their cohomology classes. In particular, we give a positive, combinatorial, geometric branching rule for computing the map in cohomology induced by the inclusion of the symplectic partial flag variety SF ( k 1 , … , k h ; n ) in the partial flag variety F ( k 1 , … , k h ; n ) . These rules have many applications in algebraic geometry, combinatorics, symplectic geometry and representation theory.