Weakly unramified representations, finite morphisms, and Knapp-Stein $R$-groups

TL;DR

This paper extends the understanding of Knapp-Stein R-groups for p-adic groups, transferring results between inner forms and providing a general structure for these groups in the context of weakly unramified characters.

Contribution

It introduces a transfer method for R-groups between quasi-split and non-quasi-split inner forms and generalizes Keys' classification to broader classes of reductive groups.

Findings

Transferred R-groups between inner forms for weakly unramified characters

Provided the structure of R-groups for general connected reductive groups

Extended classification results to non-quasi-split and more general groups

Abstract

We transfer Knapp-Stein $R$-groups for unitary weakly unramified characters between a $p$-adic quasi-split group and its non-quasi-split inner forms, and provide the structure of those $R$-groups for a general connected reductive group over a $p$-adic field. This work supports previous studies on the behavior of $R$-groups between inner forms, and extends Keys' classification for unitary unramified cases of simply-connected, almost simple, semi-simple groups.