Algorithms for computing generalized U(N) Racah coefficients

S. Gliske, W. H. Klink, T. Ton-That

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Algorithms are developed for computing generalized Racah coefficients for the U(N) groups. The irreducible representations (irreps) of the U(N) groups, as well as their tensor products, are realized as polynomials in complex variables. When tensor product irrep labels as well as a given irrep label are specified, maps are constructed from the irrep space to the tensor product space. The number of linearly independent maps gives the multiplicity. The main theorem of this paper shows that the eigenvalues of generalized Casimir operators are always sufficient to break the multiplicity. Using this theorem algorithms are given for computing the overlap between different sets of eigenvalues of commuting generalized Casimir operators, which are the generalized Racah coefficients. It is also shown that these coefficients are basis independent.

Original languageEnglish (US)
Pages (from-to)229-249
Number of pages21
JournalActa Applicandae Mathematicae
Issue number2
StatePublished - Sep 2005
Externally publishedYes


  • Algorithms
  • Generalized Casimir operators
  • Generalized Racah coefficients

ASJC Scopus subject areas

  • Applied Mathematics


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