On extensions of representations for compact Lie groups

Details On extensions of representations for compact Lie groups On extensions of representations for compact Lie groups

1999-12-22

arxiv.org/abs/math/9912180v2

J. Pure Appl. Algebra 178 (2003), no. 3, 245-254

Mathematics

Representation Theory

10 pages, AMS-LaTeX v1.2

Scientific paper

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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