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Article Dans Une Revue Journal of Combinatorial Theory, Series A Année : 2012

Co-quasi-invariant spaces for finite complex reflection groups

Résumé

We study, in a global uniform manner, the quotient of the ring of polynomials in l sets of n variables, by the ideal generated by diagonal quasi-invariant polynomials for general permutation groups W=G(r,n). We show that, for each such group W, there is an explicit universal symmetric function that gives the N^l-graded Hilbert series for these spaces. This function is universal in that its dependance on l only involves the number of variables it is calculated with. We also discuss the combinatorial implications of the observed fact that it affords an expansion as a positive coefficient polynomial in the complete homogeneous symmetric functions.
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Dates et versions

hal-00605641 , version 1 (03-07-2011)
hal-00605641 , version 2 (14-10-2011)

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Jean-Christophe Aval, François Bergeron. Co-quasi-invariant spaces for finite complex reflection groups. Journal of Combinatorial Theory, Series A, 2012, 119, pp.1432-1446. ⟨hal-00605641v2⟩

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