AVAL, Jean-Christophe; BERGERON, Nantel

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AVAL, Jean-Christophe
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Théorie des Nombres et Algorithmique Arithmétique [A2X]

BERGERON, Nantel
Department of Mathematics and Statistics [Toronto]

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Article de revue

Ce document a été publié dans

European Journal of Combinatorics. 2005, vol. 26, n° 6, p. 785-794

Elsevier

Résumé en anglais

A lattice diagram is a finite list L=((p_1,q_1),...,(p_n,q_n) of lattice cells. The corresponding lattice diagram determinant is \Delta_L(X;Y)=\det \| x_i^{p_j}y_i^{q_j} \|. These lattice diagram determinants are crucial in the study of the so-called ``n! conjecture'' of A. Garsia and M. Haiman. The space M_L is the space spanned by all partial derivatives of \Delta_L(X;Y). The ``shift operators'', which are particular partial symmetric derivative operators are very useful in the comprehension of the structure of the M_L spaces. We describe here how a Schur function partial derivative operator acts on lattice diagrams with distinct cells in the positive quadrant.< Réduire

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Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251