Green Correspondence for Virtually Pro-p Groups

TL;DR

This paper extends the Green Correspondence, a fundamental concept in modular representation theory, to the setting of finitely generated modules over completed group algebras of virtually pro-p groups, broadening its applicability.

Contribution

It establishes an analogue of the Green Correspondence specifically for finitely generated modules over completed group algebras of virtually pro-p groups, a novel extension in the field.

Findings

Proves the Green Correspondence analogue for these modules

Extends classical theory to a broader class of groups

Provides foundational results for modular representations of pro-p groups

Abstract

Let p be prime, k a finite field of characteristic p, and G a virtually pro-p group. We prove an analogue of the Green Correspondence for finitely generated modules over the completed group algebra k[[G]].