On the Schneider-Vigneras functor for principal series

TL;DR

This paper investigates the Schneider-Vigneras functor applied to principal series representations of GL_n over p-adic fields, focusing on module structures over Iwasawa algebras.

Contribution

It extends the understanding of the Schneider-Vigneras functor to irreducible modulo π principal series of GL_n(F) for any finite extension F of Q_p.

Findings

Characterization of the functor's image for these representations

Identification of module structures over the Iwasawa algebra

Insights into the representation theory of GL_n over local fields

Abstract

We study the Schneider-Vigneras functor attaching a module over the Iwasawa algebra $\Lambda(N_0)$ to a $B$-representation for irreducible modulo $\pi$ principal series of the group $\mathrm{GL}_n(F)$ for any finite field extension $F|\mathbb{Q}_p$.