EVENT DETAILS AND ABSTRACT

Title: Configurations, potentials, components and canonical bases
Speaker: Linhui Shen
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

Let $G$ be a split reductive group over $\mathbb{Q}$. We introduce a rational function $W$ on the configuration space $X:=G\backslash (G/U)^n$. By the machinery of tropicalization, it determines a set of $W$-positive tropical points of $X$. We show that the set parametrizes top components of the affine Grassmannian convolution variety. By the geometric Satake Correspondence, it parametrizes a basis in the tensor product invariants of representations of the Langlands dual group. As an application, it proves a conjecture of Joel Kamnitzer. If time permits, I will talk about its generalization to surface cases. This is a joint work with Alexander Goncharov.