Smooth admissible representations, Hom, tensor and extension of scalars

(Remark: This has previously been posted on math.stackexchange, but I believe it might be suitable for this site as well. ) Let G be a locally profinite group, and consider V and W smooth admissible representations of G over some field F (or char. 0). Let E/F be any field extension. I’d like to … Read more

Explicit formula of base change for GL(n)

Let $E/F$ be a quadratic extension of number fields and $v$ is a place of $F$. Let $\chi_1,\chi_2$ be the unramified characters of $F_v^{\times}$. If $B(\chi_1,\chi_2)$ is the unramified principal series representation of $GL_2(F_v)$, what is the $BC(\pi)$, the base change of $\pi$ to $GL_2(E_v)$? I suppose that $BC(\pi)=B(\chi_1 \circ \text{Norm}_{E_v/F_v},\chi_2 \circ \text{Norm}_{E_v/F_v})$. Is this … Read more

Automorphic representations whose local factors are tempered almost everywhere

Let F be a global field, let G be a reductive algebraic group over F, and let π be an irreducible discrete automorphic representation of G. Write π as a restricted product of local factors π=⨂νπν (here, ν ranges over the places of F), and suppose that for almost all ν, the G(Fν)-representation πν is … Read more