# SMILY: A numerical algorithm to decompose unitary representations and compute Clebsch-Gordan coefficients

@article{Ibort2016SMILYAN, title={SMILY: A numerical algorithm to decompose unitary representations and compute Clebsch-Gordan coefficients}, author={Alberto Ibort and Alberto L'opez-Yela and Julio Moro}, journal={arXiv: Mathematical Physics}, year={2016} }

A numerical algorithm that computes the decomposition of a finite-dimensional unitary reducible representation of a compact Lie group is presented. The algorithm, inspired by notions of quantum mechanics, generates two adapted states and, after appropriate algebraic manipulations, returns the block matrix structure of the representation in terms of its irreducible components. It also provides an adapted orthonormal basis. The algorithm can be used to compute the Clebsch--Gordan coefficients of…

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