Representations of the Weyl group and Wigner functions for SU(3)

Bases for SU(3) irreps are constructed on a space of three-particle tensor products of two-dimensional harmonic oscillator wave functions. The Weyl gr oup is represented as the symmetric group of permutations of the particle c oordinates of these spaces. Wigner functions for SU(3) are expressed as pro ducts of SU(2) Wigner functions and matrix elements of Weyl transformations . The constructions make explicit use of dual reductive pairs which are sho wn to be particularly relevant to problems in optics and quantum interferom etry. (C) 1999 American Institute of Physics. [S0022-2488(99)01506-6].