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.

Weighted enumerations on projective reflection groups

CASELLI, FABRIZIO;R. Biagioli
2012

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.
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/112246
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 8
social impact