Séminaire Lotharingien de Combinatoire, B08i (1984), 8 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1984, 229/S-08, p. 63-70.]

Stephen C. Milne

An Umbral Calculus for Polynomials Characterizing U(n) Tensor Products

Abstract. We continue the study of the connection between the invariant polynomials characterizing U(n) tensor operators (p,q,...,q,0,...,0), and the classical theory of symmetric functions. Those invariang polynomials arise naturally in the application of symmetry groups to mathematical physics. One such problem, with applications to spectroscopy at all levels, is the construction of a suitable basis for the set of all bounded operators mapping the set of all unitary irreducible representation spaces of the group into itself. The precise problems that give rise to those polynomials are motivated in more detail and put into a broader mathematical setting in the works of Biedenharn, Holman, Louck and the author.

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