Reduction for $SL(3)$ pre-buildings

TL;DR

This paper details the reduction process for constructing the core of an $SL(3)$ pre-building from a spectral curve, facilitating the understanding of harmonic maps with prescribed differentials.

Contribution

It provides a detailed methodology for reducing spectral curves to build $SL(3)$ pre-buildings with harmonic maps, a novel approach in geometric analysis.

Findings

Explicit reduction steps for $SL(3)$ spectral curves

Construction of pre-buildings with harmonic maps

Enhanced understanding of spectral curve geometry

Abstract

Given an $SL(3)$ spectral curve over a simply connected Riemann surface, we describe in detail the reduction steps necessary to construct the core of a pre-building with versal harmonic map whose differential is given by the spectral curve.