Weighted enumerations on projective reflection groups |
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Authors: | Riccardo Biagioli Fabrizio Caselli |
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Institution: | a Université de Lyon, Université Lyon 1, Institut Camille Jordan, UMR 5208 du CNRS, 69622 Villeurbanne, France b Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, Bologna 40126, Italy |
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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. |
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Keywords: | 05E15 |
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