Some results on Bessel functionals for GSp(4)
Number Theory
2015-01-05 v1 Representation Theory
Abstract
We prove that every irreducible, admissible representation of GSp(4,F), where F is a non-archimedean local field of characteristic zero, admits a Bessel functional, provided the representation is not one-dimensional. Given such a representation, we explicitly determine the set of all split Bessel functionals admitted by the representation, and prove that these functionals are unique. If the representation is not supercuspidal, or in an L-packet with a non-supercuspidal representation, we explicitly determine the set of all Bessel functionals admitted by the representation, and prove that these functionals are unique.
Cite
@article{arxiv.1501.00221,
title = {Some results on Bessel functionals for GSp(4)},
author = {Brooks Roberts and Ralf Schmidt},
journal= {arXiv preprint arXiv:1501.00221},
year = {2015}
}