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arXiv · 2305.02010

An extension of Steinberg's Theorem to biquotient pairs of subgroups

Marcus Zibrowius
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Abstract

We study the derived tensor product of the representation rings of subgroups of a given compact Lie group G. That is, given two such subgroups H_1 and H_2, we study the tensor product of the associated representation rings R(H_1) and R(H_2) over the representation ring RG, and prove a vanishing result for the associated higher Tor-groups. This result can be viewed as a natural generalization of the Theorem of Steinberg that asserts that the representation rings of maximal rank subgroups of G are free over RG. It my also be viewed as an analogue of a result of Singhof on the cohomology of classifying spaces. We include an immediate application to the complex K-theory of biquotient manifolds.

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Marcus Zibrowius. 2023-05-03. An extension of Steinberg's Theorem to biquotient pairs of subgroups. https://arxiv.org/abs/2305.02010

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