Discrete Components of Some Complementary Series

Details Discrete Components of Some Complementary Series Discrete Components of Some Complementary Series

2009-02-26

arxiv.org/abs/0902.4620v1

Mathematics

Representation Theory

Scientific paper

We show that complementary series representations of SO(n,1) contain discretely complementary series of SO(m,1) provided the continuous parameter is sufficiently close to the first point of reducibility and the representation of the compact part of the Levi is a sufficiently small fundamental representation. We prove as a consequence that cohomological representations of SO(n,1) of degree $i$ less than m/2 contain discretely, cohomogical representations of SO(m,1).

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