The dual of the nilradical of the parabolic subgroups of symplectic groups

Thomas Farmer

Vol. 107 (1983), No. 2, 349–368

DOI: 10.2140/pjm.1983.107.349

Abstract

For an arbitrary parabolic subgroup P of the real or complex symplectic group, let N be the nilradical. Using Kirillov theory, a subset of the dual of N is found, whose complement has Plancherel measure zero. It is shown how these representations extend by combining with the oscillator representation of a lower rank symplectic group. A result is obtained concerning the commuting algebra of the restrictions to P of the principal series representation of the symplectic group induced from a unitary character of the opposite parabolic.

Mathematical Subject Classification 2000

Primary: 22E46

Milestones

Received: 14 October 1981

Published: 1 August 1983