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Staircase Macdonald polynomials and the qDiscriminant, preprint: arXiv:0801.2443
"... We prove that a qdeformation Dk(X; q) of the powers of the discriminant is equal, up to a normalization, to a specialization of a Macdonald polynomial indexed by a staircase partition. We investigate the expansion of Dk(X; q) on different basis of symmetric functions. In particular, we show that it ..."
Abstract

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We prove that a qdeformation Dk(X; q) of the powers of the discriminant is equal, up to a normalization, to a specialization of a Macdonald polynomial indexed by a staircase partition. We investigate the expansion of Dk(X; q) on different basis of symmetric functions. In particular, we show that its expansion on the monomial basis can be explicitly described in terms of standard tableaux and we generalize a result of KingToumazetWybourne about the expansion of the qdiscriminant on the Schur basis. 1
Macdonald polynomials at t = q k
, 2008
"... 1−q k X;q,q k We investigate the homogeneous symmetric Macdonald polynomials Pλ(X;q,t) for the specialization t = qk. We show) an identity. As a conrelying the polynomials Pλ(X;q,q k) and Pλ sequence, we describe an operator whose eigenvalues characterize the polynomials Pλ(X;q,q k). 1 ..."
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1−q k X;q,q k We investigate the homogeneous symmetric Macdonald polynomials Pλ(X;q,t) for the specialization t = qk. We show) an identity. As a conrelying the polynomials Pλ(X;q,q k) and Pλ sequence, we describe an operator whose eigenvalues characterize the polynomials Pλ(X;q,q k). 1
unknown title
, 805
"... Averages of ratios of characteristic polynomials in circular βensembles and superJack polynomials ..."
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Averages of ratios of characteristic polynomials in circular βensembles and superJack polynomials