文摘
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(k1,…,kh;n) in the partial flag variety F(k1,…,kh;n). These rules have many applications in algebraic geometry, combinatorics, symplectic geometry and representation theory.