An analogue of the BGG resolution for locally analytic principal series

TL;DR

This paper constructs an exact sequence for locally analytic principal series representations of p-adic groups, extending the BGG resolution concept to the p-adic automorphic forms context.

Contribution

It introduces a novel exact sequence modelled on the dual BGG resolution for locally analytic principal series of p-adic groups.

Findings

Establishes an exact sequence involving overconvergent p-adic automorphic forms.

Provides a new tool for studying p-adic automorphic representations.

Connects representation theory with p-adic automorphic forms via an analogue of the BGG resolution.

Abstract

Let G be a connected reductive quasisplit algebraic group over a field L which is a finite extension of the p-adic numbers. We construct an exact sequence modelled on (the dual of) the BGG resolution involving locally analytic principal series representations for G(L). This leads to an exact sequence involving spaces of overconvergent p-adic automorphic forms for certain groups compact modulo centre at infinity.