Shintani relation for base change: unitary and elliptic representations
Shintani relation for base change: unitary and elliptic representations
Let $E/F$ be a cyclic extension of $p$-adic fields and $n$ a positive integer. Arthur and Clozel constructed a base change process $π\mapsto π_E$ which associates to a smooth irreducible representation of $GL_n(F)$ a smooth irreducible representation of $GL_n(E)$, invariant under $Gal(E/F)$. When $π$ is tempered, $π_E$ is tempered and …