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arXiv:1603.09673 [math.RT]AbstractReferencesReviewsResources

Parity preservation for $K$-types in an irreducible representation

Xiang Fan

Published 2016-03-31Version 1

A phenomenon of parity preservation for $K$-types occurring in an irreducible admissible representation happens for various reductive Lie groups. This note gives a uniform proof of this fact for members of real reductive dual pairs, by applying Howe's duality theory of theta correspondence.

Comments: 7 pages
Categories: math.RT
Subjects: 22E46, 11F27
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