Derived right adjoints of parabolic induction: an example

Karol Kozioł

Vol. 321 (2022), No. 2, 345–358

DOI: 10.2140/pjm.2022.321.345

Abstract

Suppose $p\ge 5$ is a prime number, and let $G={\mathrm{SL}<!--FUNCTION\; APPLICATION-->}_2({\mathbb{Q}}_p)$. We calculate the derived functors ${R<!--FUNCTION\; APPLICATION-->}^n{\mathcal{ℛ}}_B^G(\pi )$, 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 $G$.

Keywords

parabolic induction, right adjoint, mod $p$ representation theory

Mathematical Subject Classification

Primary: 22E50

Secondary: 20C08

Milestones

Received: 11 February 2022

Revised: 25 August 2022

Accepted: 4 October 2022

Published: 21 March 2023