Combinatorial Formula for the Hilbert Series of bigraded Sn-modules
نویسنده
چکیده
We introduce a combinatorial way of calculating the Hilbert series of bigraded Sn-modules as a weighted sum over standard Young tableaux in the hook shape case. This method is based on Macdonald formula for HallLittlewood polynomial and extends the result of A. Garsia and C. Procesi for the Hilbert series when q = 0. Moreover, we give the way of associating the fillings giving the monomial terms of Macdonald polynomials to the standard Young tableaux. Résumé. Nous introduisons une méthode combinatoire pour calculer la série de Hilbert de modules bigradués de Sn comme une somme pondérée sur les tableaux de Young standards à la forme crochet. Cette méthode se fonde sur la formule Macdonald pour les polynômes Hall-Littlewood et généralise un résultat de A. Garsia et C. Procesi pour la série de Hilbert dans le cas q = 0. De plus, nous proposons une méthode pour associer aux tableaux de Young standards les remplissages des monomes des polynômes de Macdonald.
منابع مشابه
A Combinatorial Formula for the Hilbert Series of Bigraded Sn-Modules
We prove a combinatorial formula for the Hilbert series of the Garsia-Haiman bigraded Sn-modules as weighted sums over standard Young tableaux in the hook shape case. This method is based on the combinatorial formula of Haglund, Haiman and Loehr for the Macdonald polynomials and extends the result of A. Garsia and C. Procesi for the Hilbert series when q = 0. Moreover, we construct an associati...
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