A new class of symmetric functions. (English) Zbl 0962.05507

Macdonald, I. G.

Sémin. Lothar. Comb. 20, B20a, 41 p. (1988).

Summary: The polynomials \(P_\lambda(q,t)\) whose algebra is discussed in this paper generalize the classical symmetric functions

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, such as the Jack symmetric functions, the Schur functions, the Hall-Littlewood functions, as well as the usual symmetric functions. The main conjecture is to prove that the entries of the transition matrix

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for going from those polynomials to (say) the Schur functions are all polynomials in \(q,t\).

MSC:

05E05

Symmetric functions and generalizations

Keywords:

Jack symmetric functions; Schur functions; Hall-Littlewood functions