Vol. 107, No. 2, 1983

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

Thomas Farmer

Vol. 107 (1983), No. 2, 349–368

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
Received: 14 October 1981
Published: 1 August 1983
Thomas Farmer