The smooth representations of GL_2(O)

TL;DR

This paper classifies smooth complex representations of GL_2 over the ring of integers in a local field, combining unpublished results of Kutzko with those of Hill to advance understanding in p-adic representation theory.

Contribution

It provides a comprehensive classification of smooth representations of GL_2(O), integrating new unpublished results with existing work to fill gaps in the literature.

Findings

Classification of smooth representations of GL_2(O) achieved

Unified framework combining Kutzko's and Hill's results

Enhanced understanding of p-adic group representations

Abstract

We present some unpublished results of Kutzko together with results of Hill, giving a classification of the smooth (complex) representations of $\mathrm{GL}_{2}(\mathcal{O})$, where $\mathcal{O}$ is the ring of integers in a local field with finite residue field.