Dominant K-theory and Integrable highest weight representations of Kac-Moody groups

Details Dominant K-theory and Integrable highest weight representations of Kac-Moody groups Dominant K-theory and Integrable highest weight representations of Kac-Moody groups

2007-09-30

arxiv.org/abs/0710.0167v2

Mathematics

Algebraic Topology

Presentation improved, small errors corrected. No change in the statements of results

Scientific paper

We give a topological interpretation of the highest weight representations of Kac-Moody groups. Given the unitary form G of a Kac-Moody group (over C), we define a version of equivariant K-theory, K_G on the category of proper G-CW complexes. We then study Kac-Moody groups of compact type in detail (see Section 2 for definitions). In particular, we show that the Grothendieck group of integrable hightest weight representations of a Kac-Moody group G of compact type, maps isomorphically onto K_G^*(EG), where $EG$ is the classifying space of proper G-actions. For the affine case, this agrees very well with recent results of Freed-Hopkins-Teleman. We also explicitly compute K_G^*(EG) for Kac-Moody groups of extended compact type, which includes the Kac-Moody group E_{10}.

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