Weihong Xu "Quantum K-theory of Incidence Varieties" (part 1)
Channel: Schubert Seminar
Date: 2022-04-03

Title: Quantum K-theory of Incidence Varieties (part 1)
Abstract: Buch, Mihalcea, Chaput, and Perrin proved that for cominuscule flag varieties, (T-equivariant) K-theoretic (3-pointed, genus 0) Gromov-Witten invariants can be computed in the (equivariant) ordinary K-theory ring. Buch and Mihalcea have a related conjecture for all type A flag varieties. In this talk, I will discuss work that proves this conjecture in the first non-cominuscule case--the incidence variety X=Fl(1,n-1;n). The proof is based on showing that Gromov-Witten varieties of stable maps to X with markings sent to a Schubert variety, a Schubert divisor, and a point are rationally connected. As applications, I will discuss positive formulas (an equivariant Chevalley formula and a non-equivariant Littlewood-Richardson rule) which determine the (equivariant) quantum K-theory ring of X. If time permits, I will state a conjectured Chevalley formula for the non-equivariant quantum K-theory ring of an arbitrary type A flag variety. The talk is based on the arxiv preprint at https://arxiv.org/abs/2112.13036.