Title: Differential identities for Schubert polynomials via pipe dreams
Speaker: Hugh Dennin (OSU)
Speaker's URL: https://math.osu.edu/people/dennin.3
Abstract: Gaetz and Gao recently proved the strong Sperner property for weak order by extending a rank-lowering operator $\nabla$, first introduced by Stanley, to an $\mathfrak{sl}_2$ poset representation. This was done by explicitly constructing the corresponding raising operator $\Delta$. Hamaker, Pechenik, Speyer, and Weigandt later showed that $\nabla$ (and hence $\Delta$) can be realized certain differential operators acting on Schubert polynomials—polynomial representatives for Schubert cycles in the cohomology of the flag variety. We outline new bijective proofs of these derivative identities for Schubert polynomials using the combinatorics of pipe dreams. These proofs extend to give related identities for $\beta$-Grothendieck polynomials.
