Dominant K-theory and integrable highest weight representations of Kac-Moody groups |
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Authors: | Nitu Kitchloo |
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Institution: | Department of Mathematics, University of California, San Diego, CA, USA |
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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 , 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 for Kac-Moody groups of extended compact type, which includes the Kac-Moody group E10. |
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Keywords: | Dominant K-theory Integrable highest weight representations Kac-Moody groups |
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