Constant Term Methods in the Theory of Tesler matrices and Macdonald Polynomial Operators
نویسندگان
چکیده
ABSTRACT The Tesler matrices with hook sums (a1, a2, . . . , an) are non-negative integral upper triangular matrices, whose i diagonal element plus the sum of the entries in the arm of its (french) hook minus the sum of the entries in its leg is equal to ai for all i. In a recent paper [6], the second author expressed the Hilbert series of the Diagonal Harmonic modules as a weighted sum of the family of Tesler matrices with hook weights (1, 1, . . . , 1). In this paper we use the constant term algorithm developed by the third author to obtain a Macdonald polynomial interpretation of these weighted sum of Tesler matrices for arbitrary hook weights. In particular we also obtain new and illuminating proofs of the results in [6].
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