The cohomology of the Quot scheme on a smooth curve as a Yangian representation

TL;DR

This paper explores how the shifted Yangian of sl_2 acts on the cohomology of Quot schemes on a smooth curve, introducing commuting operators that define a natural basis and facilitate multiplication formulas.

Contribution

It introduces a new Yangian action on Quot scheme cohomology and constructs commuting operators that produce a natural basis and multiplication formulas.

Findings

Yangian action on Quot cohomology established

Commuting operators define a natural basis

Formulas for multiplication by Segre classes derived

Abstract

We describe the action of the shifted Yangian of sl_2 on the cohomology groups of the Quot schemes of 0-dimensional quotients on a smooth projective curve. We introduce a commuting family of r operators in the positive half of the Yangian, whose action yields a natural basis of the Quot cohomology. These commuting operators further lead to formulas for the operators of multiplication by the Segre classes of the universal bundle.