On extensions of representations for compact Lie groups
Copyright policy )On extensions of representations for compact Lie groups
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.
10 pages, AMS-LaTeX v1.2
- Korean Association Of Science and Technology Studies Korea (Republic of)
- Department of Mathematics
- Korea Advanced Institute of Science and Technology Korea (Republic of)
- Korea Advanced Institute of Science and Technology Korea (Republic of)
- Korea Institute for Advanced Study Korea (Republic of)
General properties and structure of other Lie groups, Algebra and Number Theory, complex representation, FOS: Mathematics, compact Lie group, Representation Theory (math.RT), Mathematics - Representation Theory, 20C99 (Primary) 22E99 (Secondary)
General properties and structure of other Lie groups, Algebra and Number Theory, complex representation, FOS: Mathematics, compact Lie group, Representation Theory (math.RT), Mathematics - Representation Theory, 20C99 (Primary) 22E99 (Secondary)
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