Plethystic F Ormulas For
نویسندگان
چکیده
This work is concerned with the Macdonald q;t-analogue of the Kostka matrix. This matrix relates the two parameter Macdonald basis fP x; q;tg to the modiied Schur basis fS X1 , tg. The entries in this matrix, which h a v e come to be denoted by K ; q;t, h a v e been conjectured by Macdonald to be polynomials in q;t with positive i n tegral coeecients. Our main main result here is an algorithm for the construction of explicit formulas for the K ; q;t. It is shown that this algorithm yields expressions which are polynomials with integer coeecients. Recent w ork of J. Remmel shows that the resulting formulas do also yield positivity of the coeecients for a wide variety o f e n tries in the Macdonald q;t-Kostka matrix. We also obtain in this manner new explicit expressions for the Macdonald polynomials.
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