Abstract
When E=F is a quadratic extension of p-adic elds, with p6 , and H 0 is a unitary similitude group in GL(n;E) ,i t is shown that for every irreducible supercuspidal representation of GL(n;E) of lowest level the space of H 0 -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 ramied. When n is even and E=F is unramied, the space of H-invariant linear forms on the space of may have dimension two.
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