Moy-Prasad Maps for SL(2) over extensions of $Q_2$

TL;DR

This paper constructs a parametrization for characters of abelian quotients of compact subgroups of SL(2) over extensions of Q2, extending Moy-Prasad maps to fields with odd residual characteristic.

Contribution

It introduces a new parametrization for characters of compact subgroup quotients in SL(2) over certain extensions of Q2, generalizing Moy-Prasad maps.

Findings

Provides explicit parametrization for characters in the specified setting

Extends Moy-Prasad maps to fields with odd residual characteristic

Facilitates analysis of representations of SL(2) over these fields

Abstract

A parametrization for characters of abelian quotients of compact subgroups of G := SL2(F) is constructed for F an algebraic extension of Q2 that corresponds to the Moy-Prasad maps of fields of odd residual characteristic.