Let $(\pi,V)$ be a $GL_n(\mathbb{ R})$-distinguished, irreducible, admissible representation of $GL_n(\mathbb{ C})$, let $\pi'$ be an irreducible, admissible, $GL_m(\mathbb{ R})$-distinguished representation of $GL_m(\mathbb{ C})$, and let $\psi$ be a non-trival character of $\mathbb{ C}$ which is trivial on $\mathbb{ R}$. We prove that Rankin-Selberg gamma factor at $s=\frac{ 1}{ 2}$ is $\gamma(\frac{ 1}{ 2},\pi \times \pi'; \psi) = 1$. The result follows as a simple consequence from the characterisation of $GL_n(\mathbb{ R})$-distinguished representations in terms of their Langlands data.
Categories: math.RT