Dominant K-theory and Integrable highest weight representations of Kac-Moody groups
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, 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 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}.
Keywords
Cite
@article{arxiv.0710.0167,
title = {Dominant K-theory and Integrable highest weight representations of Kac-Moody groups},
author = {Nitu Kitchloo},
journal= {arXiv preprint arXiv:0710.0167},
year = {2017}
}
Comments
Update to the published version with some mistakes in Section 4 corrected. No change to the statements of the theorems