Rogers–szegö Polynomials and Hall–littlewood Symmetric Functions

Here λ denotes a partition, λ its conjugate, and the condition “λ even” (or “λ even”) implies that all parts of λ (or all parts of λ) must be even. Furthermore, sλ(x) = sλ(x1, x2, . . . ) is a Schur function of a finite or infinite number of variables. When x = (x1, . . . , xn) the identities (1.1a)–(1.1c) may be viewed as reciprocals of Weyl denominator formulas; the latter expressing the products n