Nakajima varieties and repetitive algebras

TL;DR

This paper connects Nakajima varieties of finite Dynkin type with orbit closures of repetitive algebras, revealing that certain sheaves used in quantum loop algebra representation theory are isomorphic to intersection cohomology sheaves.

Contribution

It establishes a geometric realization of Nakajima varieties as orbit closures of repetitive algebras and links perverse sheaves to intersection cohomology sheaves.

Findings

Nakajima varieties are realized as orbit closures of repetitive algebras.

Perverse sheaves for quantum loop algebras are isomorphic to intersection cohomology sheaves.

Provides a new geometric perspective on the representation theory of quantum loop algebras.

Abstract

We realize certain graded Nakajima varieties of finite Dynkin type as orbit closures of repetitive algebras of Dynkin quivers. As an application, we obtain that the perverse sheaves introduced by Nakajima for describing irreducible characters of quantum loop algebras are isomorphic to the intersection cohomology sheaves of these orbit closures.