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

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Abstract

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, KG 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 highest weight representations of a Kac-Moody group G of compact type, maps isomorphically onto over(K, ̃)G* (E G), where E G 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 KG* (E G) for Kac-Moody groups of extended compact type, which includes the Kac-Moody group E10. © 2009 Elsevier Inc. All rights reserved.

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Kitchloo, N. (2009). Dominant K-theory and integrable highest weight representations of Kac-Moody groups. Advances in Mathematics, 221(4), 1191–1226. https://doi.org/10.1016/j.aim.2009.02.006

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