Projective reflection groups have been recently defined 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 reflection groups of type G(r, p, n). In this paper we define some statistics analogous to descent number and major index over the projective reflection 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.
F. Caselli, R. Biagioli (2011). Enumerating projective reflection groups. NANCY : Assoc. Discrete Math. Theor. Comput. Sci..
Enumerating projective reflection groups
CASELLI, FABRIZIO;R. Biagioli
2011
Abstract
Projective reflection groups have been recently defined 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 reflection groups of type G(r, p, n). In this paper we define some statistics analogous to descent number and major index over the projective reflection 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.