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| Format: | Preprint |
| Published: |
2023
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| Online Access: | https://arxiv.org/abs/2305.02010 |
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| _version_ | 1866909998199603200 |
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| author | Zibrowius, Marcus |
| author_facet | Zibrowius, Marcus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02010 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An extension of Steinberg's Theorem to biquotient pairs of subgroups Zibrowius, Marcus K-Theory and Homology Algebraic Topology 19L47, 14M17, 22E15 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. |
| title | An extension of Steinberg's Theorem to biquotient pairs of subgroups |
| topic | K-Theory and Homology Algebraic Topology 19L47, 14M17, 22E15 |
| url | https://arxiv.org/abs/2305.02010 |