Matrix Factorization for an SO(2) Spinning Top and Related Problems

TL;DR

This paper explores matrix factorization related to an SO(2) spinning top using algebraic geometry, deriving explicit formulas with Riemann theta functions and discussing extensions and higher-order cases.

Contribution

It provides explicit Riemann theta function solutions for the SO(2) spinning top matrix factorization problem and discusses extensions to non-compact and higher-order cases.

Findings

Explicit Riemann theta function solutions derived

Extended analysis to non-compact and higher-order spectral cases

Enhanced understanding of algebraic-geometric methods in integrable systems

Abstract

We study the matrix factorization problem associated with an SO(2) spinning top by using the algebro-geometric approach. We derive the explicit expressions in terms of Riemann theta functions and discus some related problems including a non-compact extension and the case when the Lax matrix contains higher-order powers of the spectral parameter.