Self-dual puzzles in Schubert calculus branching

Abstract: In classical Schubert calculus, Knutson and Tao’s puzzles are a combinatorial tool that gives a positive rule for expanding the product of two Schubert classes in equivariant cohomology of the (type A) Grassmannian. I will describe a positive rule that uses self-dual puzzles to compute the restriction of a Grassmannian (type A) Schubert class to the symplectic (type C) Grassmannian in equivariant cohomology. The proof uses the machinery of quantum integrable systems. I will also discuss a generalization in which the Grassmannians are upgraded to their cotangent bundles and Schubert classes—to Segre-Schwartz-MacPherson classes. The resulting construction involves Lagrangian correspondences and produces a generalized puzzle rule with a geometric interpretation. This is joint work with Allen Knutson and Paul Zinn-Justin.

commutative algebracombinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

UC Davis algebra & discrete math seminar