Symplectic meanders

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.

KEYWORDS:

• Frobenius Lie algebra
• index
• meander
• seaweed
• symplectic Lie algebra

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B20