Abstract

When E ∕ F is a quadratic extension of p-adic fields, with p≠2, and H′ is a unitary similitude group in GL(n,E), it is shown that for every irreducible supercuspidal representation π of GL(n,E) of lowest level the space of H′-invariant linear forms has dimension at most one. The analogous fact for the corresponding unitary group H also holds, so long as n is odd or E ∕ F is ramified. When n is even and E ∕ F is unramified, the space of H-invariant linear forms on the space of π may have dimension two.

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