A new class of symmetric functions.

I will begin by reviewing briefly some aspects of the theory of symmetric functions. This will serve to fix notation and to provide some motivation for the subject of these lectures. Let x1, . . . , xn be independent indeterminates. The symmetric group Sn acts on the polynomial ring Z[x1, . . . , xn] by permuting the x’s, and we shall write Λn = Z[x1, . . . , xn] for the subring of symmetric polynomials in x1, . . . , xn. If f ∈ Λn, we may write f = ∑