Combinatorics Seminar: "Symplectic bumpless pipe dreams"

Abstract: Bumpless pipe dreams are combinatorial objects whose weighted sums give Schubert polynomials and Grothendieck polynomials. Since their introduction by Lam, Lee and Shimozono, they have been studied intensely, as it is unusual for such natural objects to appear out of thin cloth. In this talk, we introduce symplectic bumpless pipe dreams, whose weighted sums give symplectic Schubert and Grothendieck polynomials. These polynomials, indexed by fixed point free involutions, represent the classes of symplectic group orbits in the flag variety, or alternatively for skew-symmetric matrix Schubert varieties. We use these objects to prove a conjecture of Hamaker, Marberg and Pawlowski on principle specializations of these polynomials and discuss their relation to diagonal degenerations of skew-symmetric matrix Schubert varieties.

Host: Martha Precup