Degenerate Series Representations for Symplectic Groups
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We study the induced modules of real symplectic groups obtained by parabolic induction from the Siegel parabolic subgroup. The structure of the induced modules obtained from maximal parabolic subgroups of the general linear group were described by Barbasch, Sahi and Speh. We are interested in a similar description of the factors that are in the composition series of degenerate series representations of symplectic groups. More precisely, we use the τ−invariant along with the K−types of the representations to restrict the factors that can occur in the induced modules with a given wave front set. We determine the factors that occur at singular infinitesimal characters using these algebraic techniques and then use a shift functor to describe the induced modules at all infinitesimal characters. We provide a general method for computing the Langlands parameters of the factors of the induced modules and explicitly illustrate these computations for Sp(4, R) and Sp(8, R).
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73 pages
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2022-05
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Barbasch, Dan Mihai
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Speh, Birgit Else Marie
Templier, Nicolas P.
Templier, Nicolas P.
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Mathematics
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Ph. D., Mathematics
Degree Level
Doctor of Philosophy
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Attribution 4.0 International
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dissertation or thesis