Enumerating Projective Reflection Groups
Combinatorics
2011-01-20 v1
Abstract
Projective re ection groups have been recently dened by the second author. They include a special class of groups denoted G(r; p; s; n) which contains all classical Weyl groups and more generally all the complex re ection groups of type G(r; p; n). In this paper we dene some statistics analogous to descent number and major index over the projective re ection groups G(r; p; s; n), and we compute several generating functions concerning these parameters. Some aspects of the representation theory of G(r; p; s; n), as distribution of one-dimensional characters and computation of Hilbert series of invariant algebras, are also treated.
Cite
@article{arxiv.1101.3676,
title = {Enumerating Projective Reflection Groups},
author = {Riccardo Biagioli and Fabrizio Caselli},
journal= {arXiv preprint arXiv:1101.3676},
year = {2011}
}