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.
2011
23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
147
158
F. Caselli, R. Biagioli (2011). Enumerating projective reflection groups. NANCY : Assoc. Discrete Math. Theor. Comput. Sci..
F. Caselli; R. Biagioli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/117265
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