Distinguished representations of $GL(n,\mathbb{C})$

Let $V$ be a $GL_n(\mathbb{R})$-distinguished, irreducible, admissible representation of $GL_n(\mathbb{C})$. We prove that any continuous linear functional on $V$, which is invariant under the action of the real mirabolic subgroup, is automatically $GL_n(\mathbb{R})$-invariant.

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