Loop groups and twisted K-theory III

• 成果类型: Article
• 署名作者: Freed, Daniel S.; Hopkins, Michael J.; Teleman, Constantin
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.174.2.5
• 发表日期: 2011
• 页码: 947-1007
• 关键词: euler number multiplets; connected lie-groups; character formula; dirac operator; REPRESENTATIONS; COHOMOLOGY; ALGEBRAS; bundles

摘要

In this paper, we identify the Ad-equivariant twisted K-theory of a compact Lie group G with the Verlinde group of isomorphism classes of admissible representations of its loop groups. Our identification preserves natural module structures over the representation ring R(G) and a natural duality pairing. Two earlier papers in the series covered foundations of twisted equivariant K-theory, introduced distinguished families of Dirac operators and discussed the special case of connected groups with free pi(1). Here, we recall the earlier material as needed to make the paper self-contained. Going further, we discuss the relation to semi-infinite cohomology, the fusion product of conformal field theory, the role of energy and a topological Peter-Weyl theorem.