Central characters for smooth irreducible modular representations of GL_2(Q_p)

TL;DR

This paper proves that all smooth irreducible representations of GL_2(Q_p) over an algebraic closure of F_p have a central character, advancing understanding of their structure.

Contribution

It establishes that every smooth irreducible F_p^alg-linear representation of GL_2(Q_p) admits a central character, a previously unresolved property.

Findings

Every such representation admits a central character

Clarifies the structure of smooth irreducible representations

Provides a foundation for further classification

Abstract

We prove that every smooth irreducible F_p^alg-linear representation of GL_2(Q_p) admits a central character.