Jia-Rui Fei

Cluster Geometry of Universal Schubert Polynomials I: Geometric Bases and Schubert Transitions

We study Fulton's universal Schubert polynomials $\mathfrak S_w(c)$ as regular functions on the upper unitriangular group $U_N$. The standard triangular cluster structure associates a Schubert $\sf g$-vector to every permutation. Their convex hull is unimodularly equivalent to $\Delta_1\times\cdots\times\Delta_{N-1}$,...