Symplectic Restriction Varieties and Geometric Branching Rules
نویسنده
چکیده
In this paper, we introduce new, combinatorially defined subvarieties of isotropic Grassmannians 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 i : SG(k, n)→ G(k, n). This rule has many applications in algebraic geometry, symplectic geometry, combinatorics, and representation theory. In the final section of the paper, we discuss the rigidity of Schubert classes in the cohomology of SG(k, n). Symplectic restriction varieties, in certain instances, give explicit deformations of Schubert varieties, thereby showing that the corresponding classes are not rigid.
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