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

2007/09/30 by Nitu Kitchloo, Kitchloo, Nitu
Mathematics · #17B67 #19L47 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.0710.0167

openalex publication_date 2007/09/30 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We give a topological interpretation of the highest weight representations of\nKac-Moody groups. Given the unitary form G of a Kac-Moody group (over C), we\ndefine a version of equivariant K-theory, K_G on the category of proper G-CW\ncomplexes. We then study Kac-Moody groups of compact type in detail (see\nSection 2 for definitions). In particular, we show that the Grothendieck group\nof integrable hightest weight representations of a Kac-Moody group G of compact\ntype, maps isomorphically onto K_G^*(EG), where EG is the classifying space\nof proper G-actions. For the affine case, this agrees very well with recent\nresults of Freed-Hopkins-Teleman. We also explicitly compute K_G^*(EG) for\nKac-Moody groups of extended compact type, which includes the Kac-Moody group\nE₁₀.\n

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