On the degenerate principal series of complex symplectic groups

Details On the degenerate principal series of complex symplectic groups On the degenerate principal series of complex symplectic groups

2011-11-16

arxiv.org/abs/1111.3915v3

Mathematics

Representation Theory

19 pages, 1 figure. Bibliography updated, typos corrected. Final version, to appear in J. Funct. Anal

Scientific paper

We apply techniques introduced by Clerc, Kobayashi, Orsted and Pevzner to study the degenerate principal series of Sp(n,C). An explicit description of the K-types is provided and Knapp-Stein normalised operators are realised a symplectic Fourier transforms, and their K-spectrum explicitely computed. Reducibility phenomena are analysed in terms of K-types and eigenvalues of intertwining operators. We also construct a new model for these representations, in which Knapp-Stein intertwiners take an algebraic form.

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