Algorithms for computing generalized U(N) Racah coefficients

Acta Applicandae Mathematicae

Volumn 88, Issue 2, 2005, Pages 229-249

  Gliske, S ^a   Klink, W H ^a   Ton That, T ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

Algorithms; Generalized Casimir operators; Generalized Racah coefficients

Indexed keywords

CALCULATIONS; EIGENVALUES AND EIGENFUNCTIONS; MAPS; TENSORS; THEOREM PROVING;

GENERALIZED CASIMIR OPERATORS; GENERALIZED RACAH COEFFICIENTS; OVERLAP;

ALGORITHMS;

EID: 24344494383     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10440-005-8345-2     Document Type: Article

References (11)

1. Aulwes, R. T., Klink, W. H. and Ton-That, T.: J. Phys. A 34 (2001), 8237.
2. Godement, R.: Introduction a la theorie des groupes de Lie, Publ. Math. Univ. Paris, Universite de Paris VII, Paris, 1982, Theorem 2, p. 580.
3. Multiplicity can be computed using Steinberg's formula, see Humphreys, J.: Introduction to Lie Algebras and Representation Theory, Springer-Verlag, Berlin, 1972, page 141.
4. Klink, W. H. and Ton-That, T.: J. Phys. A 21 (1988), 3877.
5. Klink, W. H. and Ton-That, T.: J. Funct. Anal. 84 (1989), 1.
6. Klink, W. H. and Ton-That, T.: J. Comput. Phys. 80 (1989), 453.
7. Klink, W. H. and Ton-That, T.: J. Algebra 145 (1992), 187.
8. Klink, W. H., Ton-That, T. and Wills, R. D.: J. Phys. A 26 (1993), 3229.
9. Borel Weil theory is discussed in Knapp, A.: Representation Theory of Semisimple Lie Groups, Princeton University Press, Princeton, NJ, 1986, page 143.
10. See for example, Thompson, W. J.: Anglular Momentum, An Illustrated Guide to Rotational Symmetries for Physical Systems, Wiley-Interscience, New York, 1994, a text that is accompanied by a diskette for comuting various SU(2) coefficients.
11. See for example, Varshalovich, D. A., Moskalev, A. N. and Khersonskii, V. K.: Quantum Theory of Angular Momentum, World Scientific Publishing, Singapore, 1988.