Determinantal expressions for Macdonald polynomials

Details Determinantal expressions for Macdonald polynomials Determinantal expressions for Macdonald polynomials

1998-08-11

arxiv.org/abs/math/9808050v1

Mathematics

Combinatorics

21 pages, TeX, to be published in IMRN

Scientific paper

We show that the action of classical operators associated to the Macdonald
polynomials on the basis of Schur functions, S_{\lambda}[X(t-1)/(q-1)], can be
reduced to addition in \lambda-rings. This provides explicit formulas for the
Macdonald polynomials expanded in this basis as well as in the ordinary Schur
basis, S_{\lambda}[X], and the monomial basis, m_{\lambda}[X].

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