SU(N) Meander Determinants

TL;DR

This paper generalizes the concept of meanders to SU(N) groups, providing explicit formulas for their determinants by extending algebraic frameworks from SU(2) to SU(N).

Contribution

It introduces a novel SU(N) generalization of meanders and derives explicit formulas for their determinants, expanding algebraic and combinatorial understanding.

Findings

Derived explicit formulas for SU(N) meander determinants.

Extended the Temperley-Lieb algebra framework to SU(N).

Provided a new algebraic approach to analyze meander configurations.

Abstract

We propose a generalization of meanders, i.e., configurations of non-selfintersecting loops crossing a line through a given number of points, to SU(N). This uses the reformulation of meanders as pairs of reduced elements of the Temperley-Lieb algebra, a SU(2)-related quotient of the Hecke algebra, with a natural generalization to SU(N). We also derive explicit formulas for SU(N) meander determinants, defined as the Gram determinants of the corresponding bases of the Hecke algebra.