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

Author:

Alina Marian, Andrei Neguţ

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Representation Theory (math.RT)

journal:

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date:

2023-07-24 16:00:00

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.