A stable splitting for spaces of commuting elements in unitary groups

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-02-19 DOI:10.1112/jlms.70084

Alejandro Adem, José Manuel Gómez, Simon Gritschacher

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引用次数: 0

Abstract

We prove an analogue of Miller's stable splitting of the unitary group $U (m)$ for spaces of commuting elements in $U (m)$ . After inverting $m!$ , the space $Hom (Z^{n}, U (m))$ splits stably as a wedge of Thom-like spaces of bundles of commuting varieties over certain partial flag manifolds. Using Steenrod operations, we prove that our splitting does not hold integrally. Analogous decompositions for symplectic and orthogonal groups as well as homological results for the one-point compactification of the commuting variety in a Lie algebra are also provided.

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.