Symplectic meanders

TL;DR

This paper introduces symplectic meanders, a graphical tool for computing the index of seaweed subalgebras in sp(2n), simplifying the process through combinatorial methods and explicit formulas.

Contribution

It develops symplectic meanders as a novel graphical approach for calculating indices of seaweed subalgebras in symplectic Lie algebras, extending previous work on sl(n).

Findings

Index can be computed by counting connected components of symplectic meanders.

Formulas for the index are derived in terms of elementary functions in certain cases.

Symplectic meanders provide a combinatorial framework for understanding seaweed subalgebras.

Abstract

Analogous to the sl(n) case, we address the computation of the index of seaweed subalgebras of sp(2n) by introducing graphical representations called symplectic meanders. Formulas for the algebra's index may be computed by counting the connected components of its associated meander. In certain cases, formulas for the index can be given in terms of elementary functions.