Neil Fan, part1, Bumpless Pipe Dream Fragments—Equivariant Geometry of Clans скачать в хорошем качестве

Neil Fan, part1, Bumpless Pipe Dream Fragments—Equivariant Geometry of Clans

Title: Bumpless Pipe Dream Fragments—Equivariant Geometry of Clans Abstract: In this talk, we introduce clan polynomials as the weight generating function of bumpless pipe dream fragments. It turns out that clan polynomials arise naturally in the equivariant geometry of ($GL_p\times GL_q$)-orbits over the flag variety $Fl_{p+q}$ parametrized by $(p,q)$-clans. Furthermore, we show that the coefficients in the equivariant Schubert expansion of the fundamental classes of ($GL_p\times GL_q$)-orbit closures are exactly clan polynomials, which resolves an open problem posed by Wyser and Yong. This talk is based on joint work with Yiming Chen, Rui Xiong and Ming Yao.