Equivariant quantum cohomology of cotangent bundle of $G/P$

TL;DR

This paper establishes a connection between the quantum multiplication by divisors in the cotangent bundle of a flag variety and stable basis, confirming a conjectured formula through algebraic and geometric techniques.

Contribution

It identifies the quantum multiplication in cotangent bundles of flag varieties using stable basis and verifies a conjectured formula by Braverman.

Findings

Quantum multiplication by divisors is expressed via stable basis.

The formula is shown to be conjugate to Braverman's conjecture.

The approach combines stable basis techniques with restriction formulas.

Abstract

Let $G$ denote a complex semisimple linear algebraic group, $P$ a parabolic subgroup of $G$ and $\mathcal{P}=G/P$. We identify the quantum multiplication by divisors in $T^*\mathcal{P}$ in terms of stable basis, which is introduced by Maulik and Okounkov. Using this and the restriction formula for stable basis, we show that the $G\times\mathbb{C}^*$-equivariant quantum multiplication formula in $T^*\mathcal{P}$ is conjugate to the conjectured formula by Braverman.