Meanders and the Temperley-Lieb algebra

Details Meanders and the Temperley-Lieb algebra Meanders and the Temperley-Lieb algebra

1996-02-06

arxiv.org/abs/hep-th/9602025v1

Commun.Math.Phys. 186 (1997) 1-59

Physics

High Energy Physics

High Energy Physics - Theory

85p, uuencoded, uses harvmac (l mode) and epsf, 88 figures

Scientific paper

The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weight $q$ per connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram determinant as a function of $q$, and make use of the orthogonalization process to derive alternative expressions for meander numbers as sums over correlated random walks.

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