Quiver varieties and tensor products

• 成果类型: Article
• 署名作者: Nakajima, H
• 署名单位: Kyoto University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/PL00005810
• 发表日期: 2001
• 页码: 399-449
• 关键词: affine algebras; instantons; SPACES

摘要

In this article, we give geometric constructions of tensor products in various categories using quiver varieties. More precisely, we introduce a lagrangian subvariety (3) over tilde in a quiver variety. and show the following results: (1) The homology group of (3) over tilde is a representation of a symmetric Kac-Moody Lie algebra g, isomorphic to the tensor product V(lambda (1)) circle times (...)circle times V(lambda (N)) of integrable highest weight modules. (2) The set of irreducible components of (3) over tilde has a structure of a crystal, isomorphic to that of the q-analogue of V(lambda (1)) circle times (...)circle times V(lambda (N)). (3) The equivariant K-homology group of (3 ) over tilde is isomorphic to the tensor product of universal standard modules of the quantum loop algebra U-q(Lg), when g is of type ADE. We also give a purely combinatorial description of the crystal of (2). This result is new even when N = 1.