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Recurrence relation for the 6j-symbol of su_q(2) as a symmetric eigenvalue problem

Igor Khavkine

Department of Mathematics, University of Trento, I–38123 Povo (TN), Italy

TIFPA-INFN, Trento, Italy

https://doi.org/10.1142/S0219887815501170Cited by:4 (Source: Crossref)

Abstract

A well-known recurrence relation for the 6j-symbol of the quantum group su_q(2) is realized as a tridiagonal, symmetric eigenvalue problem. This formulation can be used to implement an efficient numerical evaluation algorithm, taking advantage of existing specialized numerical packages. For convenience, all formulas relevant for such an implementation are collected in Appendix A. This realization is a byproduct of an alternative proof of the recurrence relation, which generalizes a classical (q = 1) result of Schulten and Gordon and uses the diagrammatic spin network formalism of Temperley–Lieb recoupling theory to simplify intermediate calculations.

Keywords:

AMSC: 20G05, 20G42, 65Q30, 65F15

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