Nakajima varieties and repetitive 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.

26 pages, v2 : Minor corrections. Final version to appear in PRIMS (Publications of the Research Institute for Mathematical Sciences, Kyoto)