On the degenerate principal series of complex symplectic groups

Pierre Clare

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arXiv · 1111.3915

On the degenerate principal series of complex symplectic groups

Pierre Clare

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Abstract

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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Pierre Clare. 2011-11-16. On the degenerate principal series of complex symplectic groups. https://arxiv.org/abs/1111.3915

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