U(N) WIGNER COEFFICIENTS, THE PATH SUM FORMULA, AND INVARIANT G-FUNCTIONS Academic Article uri icon

abstract

  • We prove the path sum formula for computing the U(n) invariant denominator functions associated to stretched U(n) Wigner operators. A family of U(n) invariant polynomials G[](n) is then defined which generalize the Gq(n) polynomials previously studied. The G[](n) polynomials are shown to satisfy a number of difference equations and have symmetry properties similar to the Gq(n) polynomials. We also give a direct proof of the important transposition symmetry for the G[](n) polynomials. To enable the non-specialist to understand the foundations for these remarkable polynomials, we provide an exposition of the boson calculus and the construction of the multiplicity-free U(n) Wigner operators. 1985.

published proceedings

  • ADVANCES IN APPLIED MATHEMATICS

author list (cited authors)

  • BIEDENHARN, L. C., GUSTAFSON, R. A., & MILNE, S. C.

citation count

  • 8

complete list of authors

  • BIEDENHARN, LC||GUSTAFSON, RA||MILNE, SC

publication date

  • January 1985