Derived right adjoints of parabolic induction: an example

Abstract

Suppose $p\ge 5$ is a prime number, and let $G={\text{SL}}_2({\mathbb{Q}}_p)$. We calculate the derived functors ${\text{R}}^n{\mathcal{R}}_B^G(\pi )$, where $B$ is a Borel subgroup of $G$, ${\mathcal{R}}_B^G$ is the right adjoint of smooth parabolic induction constructed by Vignéras, and $\pi$ is any smooth, absolutely irreducible, mod $p$ representation of $G$.

9 pages. v2: Minor changes. To appear in PJM

References in corpus (2)

• Parabolic induction and extensions
• Functorial properties of pro-$p$-Iwahori cohomology