Kac-Moody群的支配K-理论与可积最高权表示
Dominant K-theory and Integrable highest weight representations of Kac-Moody groups
摘要：
给出了Kac-Moody群的最高权表示的拓扑解释.给定C上Kac-Moody群的酉形式G，在真G-CW复形范畴上定义了一个等变K-理论的版本K_G.然后我们详细研究紧型的Kac-Moody群（定义见第2节）。特别地，我们证明了紧型Kac-Moody群G的可积最高权表示的Grothendieck群同构映射到K_G^*（EG）上，其中$EG$是真G-作用的分类空间.对于仿射情形，这与Freed-Hopkins-Teleman最近的结果非常一致。我们还显式地计算了扩张紧型Kac-Moody群的K_G^*（EG），其中包括Kac-Moody群E_{10} .
英文摘要：
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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