English

On the degenerate principal series of complex symplectic groups

Representation Theory 2012-02-20 v3

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.

Keywords

Cite

@article{arxiv.1111.3915,
  title  = {On the degenerate principal series of complex symplectic groups},
  author = {Pierre Clare},
  journal= {arXiv preprint arXiv:1111.3915},
  year   = {2012}
}

Comments

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