Test Vectors for Archimedean Period Integrals
Test Vectors for Archimedean Period Integrals
We study period integrals involving Whittaker functions associated to generic irreducible Casselman-Wallach representations of $\mathrm{GL}_n(F)$, where $F$ is an archimedean local field. Via the archimedean theory of newforms for $\mathrm{GL}_n$ developed by the first author, we prove that newforms are weak test vectors for several period integrals, including the $\mathrm{GL}_n …