The canonical resolution of the multiplicity problem for U(3): An explicit and complete constructive solution

  • L. C. Biedenharn
  • M. A. Lohe
  • J. D. Louck
Mathematical Physics
Part of the Lecture Notes in Physics book series (LNP, volume 50)


The multiplicity problem for tensor operators in U(3) has a unique (canonical) resolution which we utilize to effect the explicit construction of all U(3) Wigner and Racah coefficients. We employ methods which elucidate the structure of the results; in particular, we describe the significance of the denominator functions entering the structure of these coefficients, and the relation of these denominator functions to the null space of the canonical tensor operators. An interesting feature of the denominator functions is the appearance of new, group theoretical, polynomials exhibiting several remarkable and quite unexpected.


Null Space Weight Space Linear Factor Tensor Operator Operator Pattern 
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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • L. C. Biedenharn
    • 1
  • M. A. Lohe
    • 2
  • J. D. Louck
    • 3
  1. 1.Department of PhysicsDuke UniversityGermany
  2. 2.Department of PhysicsDuke UniversityGermany
  3. 3.Theoretical Division, Los Alamanos Scientific LaboratoryUniversity of CaliforniaLos AlamosGermany

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