Quiver varieties and t-analogs of q-characters of quantum affine algebras

• 成果类型: Article
• 署名作者: Nakajima, H
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2004.160.1057
• 发表日期: 2004
• 页码: 1057-1097
• 关键词: finite-dimensional representations; kac-moody algebras; ale spaces; bases; instantons; conjecture; yangians

摘要

We consider a specialization of an untwisted quantum affine algebra of type ADE at a nonzero complex number, which may or may not be a root of unity. The Grothendieck ring of its finite dimensional representations has two bases, simple modules and standard modules. We identify entries of the transition matrix with special values of computable polynomials, similar to Kazhdan-Lusztig polynomials. At the same time we compute q-characters for all simple modules. The result is based on computations of Betti numbers of graded/cyclic quiver varieties. (The reason why we use will be explained at the end of the introduction.)