#####
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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