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

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.