We show that the number of fully packed loop configurations corresponding to a matching with m nested arches is polynomial in m if m is large enough, thus essentially proving two conjectures by Zuberâ€¦ (More)

Let W be a classical Weyl group, that is, W is either the symmetric group An 1, the hyperoctahedral group Bn, or the even-signed permutation group Dn. Consider the natural diagonal and tensor actionsâ€¦ (More)

An explicit formula expressing the coefficients of tháº½ R-polynomials as a linear combinations of those of the corresponding R-polynomials is given. Several sys tems of inequalitie s satisfied by theâ€¦ (More)

A class of partially ordered sets called diamonds, that includes all Coxeter groups ordered by Bruhat order, is introduced. It is shown that the definition of Kazhdan-Lusztig polynomials can beâ€¦ (More)

We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all nonâ€¦ (More)

A finite subgroup of GL(n, C) is involutory if the sum of the dimensions of its irreducible complex representations is given by the number of absolute involutions in the group. A uniformâ€¦ (More)

In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370â€“393] there is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflectionâ€¦ (More)

Combinatorial aspects of multivariate diagonal invariants of the symmetric group are studied. As a consequence we deduce the existence of a multivariate extension of the classical Robinson-Schenstedâ€¦ (More)

We find an explicit formula for the Kazhdan-Lusztig polynomials Pui,a ,vi of the symmetric group S(n) where, for a, i, n âˆˆ N such that 1 â‰¤ a â‰¤ i â‰¤ n, we denote by ui,a = sasa+1 Â· Â· Â· siâˆ’1 and by viâ€¦ (More)