A class of perverse sheaves on framed representation varieties of the Jordan quiver

TL;DR

This paper introduces a new class of perverse sheaves on framed Jordan quiver representation varieties and explores their connections with symmetric groups, Schur algebras, and Fock spaces.

Contribution

It defines a novel class of perverse sheaves and investigates their relationships with key algebraic structures, advancing understanding in geometric representation theory.

Findings

Established a link between perverse sheaves and symmetric group products.

Connected the sheaves to tensor products of Schur algebras.

Related the sheaves to tensor products of Fock spaces.

Abstract

A class of perverse sheaves on framed representation varieties of the Jordan quiver is defined. Its relationship with product of symmetric groups, tensor product of Schur algebras, and tensor product of Fock spaces are addressed.