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On extensions of representations for compact Lie groups

Jin-Hwan Cho·Min Kyu Kim·Dong Youp Suh
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Abstract

Let $H$ be a closed normal subgroup of a compact Lie group $G$ such that $G/H$ is connected. This paper provides a necessary and sufficient condition for every complex representation of $H$ to be extendible to $G$, and also for every complex $G$-vector bundle over the homogeneous space $G/H$ to be trivial. In particular, we show that the condition holds when the fundamental group of $G/H$ is torsion free.

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Jin-Hwan Cho, Min Kyu Kim, Dong Youp Suh. 1999-12-22. On extensions of representations for compact Lie groups. https://doi.org/10.1016/s0022-4049(02)00212-8

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