Determinantal expressions for Macdonald polynomials
L. Lapointe, A. Lascoux, J. Morse
Abstract
We show that the action of classical operators associated to the Macdonald polynomials on the basis of Schur functions, Sλ[X(t-1)/(q-1)], can be reduced to addition in λ-rings. This provides explicit formulas for the Macdonald polynomials expanded in this basis as well as in the ordinary Schur basis, Sλ[X], and the monomial basis, mλ[X].
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