Moduli of Flags of Sheaves and their K-theory

TL;DR

This paper introduces new moduli spaces of flags of sheaves on P^2 and demonstrates how they induce algebraic actions on K-theory, linking geometric structures with algebraic operations.

Contribution

It constructs moduli spaces of flags of sheaves on P^2 and establishes explicit formulas for algebra actions on their K-theory, advancing the understanding of geometric representation theory.

Findings

Defined moduli spaces of flags of sheaves on P^2

Established functors between derived categories of sheaf moduli spaces

Derived explicit formulas for shuffle algebra actions on K-theory

Abstract

We introduce moduli spaces of flags of sheaves on P^2, and use them to obtain functors between the derived categories of the usual moduli spaces of sheaves on P^2. These functors induce an action of the shuffle algebra on K-theory, by certain explicit formulas.