Riccardo Biagioli ; Fabrizio Caselli - Enumerating projective reflection groups

dmtcs:2898 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2898
Enumerating projective reflection groups

Authors: Riccardo Biagioli ; Fabrizio Caselli

    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 some invariant algebras, are also treated.


    Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
    Section: Proceedings
    Published on: January 1, 2011
    Imported on: January 31, 2017
    Keywords: reflection groups,characters,permutation statistics,generating functions,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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