# Equivariant quantum differential equation, Stokes bases, and K-theory for a projective space

## TL;DR

This paper studies the equivariant quantum differential equation for projective space, establishing an equivariant gamma theorem, describing Stokes bases via K-theory, and extending classical results to an equivariant setting.

## Contribution

It introduces an equivariant gamma theorem and characterizes Stokes bases in terms of equivariant K-theory, extending Dubrovin and Guzzetti's classical results.

## Key findings

- Proves an equivariant gamma theorem for projective space.
- Describes Stokes bases using equivariant K-theory and braid group actions.
- Provides an equivariant extension of known quantum differential equation results.

## Abstract

We consider the equivariant quantum differential equation for the projective space $P^{n-1}$. We prove an equivariant gamma theorem for $P^{n-1}$, which describes the asymptotics of the differential equation at its regular singular point in terms of the equivariant characteristic gamma class of the tangent bundle of $P^{n-1}$. We describe the Stokes bases of the differential equation at its irregular singular point in terms of the exceptional bases of the equivariant K-theory algebra of $P^{n-1}$ and a suitable braid group action on the set of exceptional bases. Our results are an equivariant version of the well-know results of B. Dubrovin and D. Guzzetti.