Restrictions of the Complementary Series of the Universal Covering of the Symplectic Group

Details Restrictions of the Complementary Series of the Universal Covering of the Symplectic Group Restrictions of the Complementary Series of the Universal Covering of the Symplectic Group

2006-09-15

arxiv.org/abs/math/0609430v4

Journal of Lie Theory 20 No 1 31-48 (2010)

Mathematics

Representation Theory

15 pages, 1 figure (not included due to technical difficulties with arxiv.org)

Scientific paper

We study the restrictions of certain degenerate principal series
representations of the universal covering of the symplectic group. We construct
an isometry between the complementary series and the unitary principal series
which preserves the action of a symplectic subgroup no bigger than half of the
size of the original group.

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