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An extension of Steinberg's theorem to biquotient pairs of subgroups.

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Τίτλος: An extension of Steinberg's theorem to biquotient pairs of subgroups.
Συγγραφείς: Zibrowius, M.1 (AUTHOR) marcus.zibrowius@hhu.de
Πηγή: Compositio Mathematica. May2026, Vol. 162 Issue 5, p1159-1179. 21p.
Θεματικοί όροι: *Tensor products, *Representations of groups (Algebra), *Semisimple Lie groups, *K-theory
Περίληψη: 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 upper H 1 H 1 $H_1$ and upper H 2 H 2 $H_2$ , we study the tensor product of the associated representation rings normal upper R upper H 1 R H 1 $\mathrm{R}H_1$ and normal upper R upper H 2 R H 2 $\mathrm{R}H_2$ over the representation ring normal upper R upper G R G $\mathrm{R}G$ , and prove a vanishing result for the associated higher Tor groups. This result can be viewed as a natural extension of the Theorem of Steinberg that asserts that the representation rings of maximal rank subgroups of G are free over normal upper R upper G R G $\mathrm{R}G$. It may 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. [ABSTRACT FROM AUTHOR]
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  Data: An extension of Steinberg's theorem to biquotient pairs of subgroups.
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  Data: <searchLink fieldCode="AR" term="%22Zibrowius%2C+M%2E%22">Zibrowius, M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> marcus.zibrowius@hhu.de</i>
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  Data: <searchLink fieldCode="JN" term="%22Compositio+Mathematica%22">Compositio Mathematica</searchLink>. May2026, Vol. 162 Issue 5, p1159-1179. 21p.
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– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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 upper H 1 H 1 $H_1$ and upper H 2 H 2 $H_2$ , we study the tensor product of the associated representation rings normal upper R upper H 1 R H 1 $\mathrm{R}H_1$ and normal upper R upper H 2 R H 2 $\mathrm{R}H_2$ over the representation ring normal upper R upper G R G $\mathrm{R}G$ , and prove a vanishing result for the associated higher Tor groups. This result can be viewed as a natural extension of the Theorem of Steinberg that asserts that the representation rings of maximal rank subgroups of G are free over normal upper R upper G R G $\mathrm{R}G$. It may 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. [ABSTRACT FROM AUTHOR]
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        Value: 10.1017/S0010437X26103194
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              Text: May2026
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