  We attempt to explain the ubiquity of tableaux and of Pieri and Cauchy
formulae for combinatorially defined families of symmetric functions. We show
that such formulae are to be expected from symmetric functions arising from
representations of Heisenberg algebras. The resulting framework that we
describe is a generalization of the classical Boson-Fermion correspondence,
from which Schur functions arise. Our work can be used to understand
Hall-Littlewood polynomials, Macdonald polynomials and Lascoux, Leclerc and
Thibon's ribbon functions, together with other new families of symmetric
functions.
