arXiv subjects

Fabrizio Caselli

Publications and source records attributed to Fabrizio Caselli.

23 records · Page 2Linked to original sources

arXiv2010

Refined Gelfand models for wreath products

In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] it is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. This model can be naturally decomposed into the direct sum of submodules indexed by symmetric conjugacy classes, and in this paper we present a simple combinatorial description of the irreducible decomposition of these submodules if the group is the wreath product of a cyclic group with a symmetric group. This is attained by showing that such decomposition is compatible with the generalized Robinson-Schensted correspondence for these groups.

math.CO↗

arXiv2009

Involutory reflection groups and their models

A finite subgroup of $GL(n,\mathbb C)$ 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 uniform combinatorial model is constructed for all non-exceptional irreducible complex reflection groups which are involutory including, in particular, all infinite families of finite irreducible Coxeter groups.

math.CO↗

arXiv2009

Projective reflection groups

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 non exceptional irreducible complex reflection groups find a natural description in this wider setting.

math.CO↗

arXiv2008

Diagonal invariants and the refined multimahonian distribution

Combinatorial aspects of multivariate diagonal invariants of the symmetric group are studied. As a consequence it is proved the existence of a multivariate extension of the classical Robinson-Schensted correspondence. Further byproduct are a pure combinatorial algorithm to describe the irreducible decomposition of the tensor product of two irreducible representations of the symmetric group, and new symmetry results on permutation enumeration with respect to descent sets.

math.CO↗

arXiv2005

On the number of fully packed loop configurations with a fixed associated matching

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 Zuber [Electronic J. Combin. 11 (2004), Article #R13].

math.CO↗