Stabilizers of quadratic points on the Bruhat-Tits tree of SL(2) over finite extensions of Q2

TL;DR

This paper computes the stabilizers of quadratic points on the Bruhat-Tits tree of SL(2) over finite extensions of Q2, providing explicit descriptions of these stabilizers in the context of local field extensions.

Contribution

It explicitly determines the stabilizers of quadratic points in the Bruhat-Tits tree for SL(2) over finite extensions of Q2, a previously uncharacterized aspect.

Findings

Explicit stabilizer descriptions for quadratic points

Enhanced understanding of local field extension actions

Applications to representation theory of p-adic groups

Abstract

For F, a finite extension of Q2, and E a quadratic extension of F, I compute the stabilizer in SL(2,F} of a point in the Bruhat-Tits tree of SL(2,E).