A note on quivers with symmetries

Abstract

We show that the bases of irreducible integrable highest weight module of a non-symmetric Kac-Moody algebra, which is associated to a quiver with a nontrivial admissible automorphism, can be naturally identified with a set of certain invariant Langrangian irreducible subvarieties of certain varieties associated with the quiver defined by Nakajima. In the case of non-symmetric affine or finite Kac-Moody algebras, the bases can be naturally identified with a set of certain invariant Langrangian irreducible subvarieties of a particular deformation of singularities of the moduli space of instantons over A-L-E spaces. The motivation of this paper comes from string/string duality and the paper is ended with questions and speculations related to string/string duality.

16 pages, AMS-LATEX file

References in corpus (2)

• The SO(32) Heterotic String on a K3 Surface
• Evidence for S-Duality in N=4 Supersymmetric Gauge Theory

Cited by in corpus (3)

• Quiver varieties and tensor products
• Diagram automorphisms of quiver varieties
• A modification of the Anderson-Mirkovic conjecture for Mirkovic-Vilonen polytopes in types B and C