666 research outputs found

    Iterated wreath product of the simplex category and iterated loop spaces

    Get PDF
    Generalising Segal's approach to 1-fold loop spaces, the homotopy theory of nn-fold loop spaces is shown to be equivalent to the homotopy theory of reduced Θn\Theta_n-spaces, where Θn\Theta_n is an iterated wreath product of the simplex category Δ\Delta. A sequence of functors from Θn\Theta_n to Γ\Gamma allows for an alternative description of the Segal-spectrum associated to a Γ\Gamma-space. In particular, each Eilenberg-MacLane space K(π,n)K(\pi,n) has a canonical reduced Θn\Theta_n-set model

    Generalized iterated wreath products of cyclic groups and rooted trees correspondence

    Full text link
    Consider the generalized iterated wreath product Zr1≀Zr2≀…≀Zrk\mathbb{Z}_{r_1}\wr \mathbb{Z}_{r_2}\wr \ldots \wr \mathbb{Z}_{r_k} where ri∈Nr_i \in \mathbb{N}. We prove that the irreducible representations for this class of groups are indexed by a certain type of rooted trees. This provides a Bratteli diagram for the generalized iterated wreath product, a simple recursion formula for the number of irreducible representations, and a strategy to calculate the dimension of each irreducible representation. We calculate explicitly fast Fourier transforms (FFT) for this class of groups, giving literature's fastest FFT upper bound estimate.Comment: 15 pages, to appear in Advances in the Mathematical Science

    Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

    Full text link
    Consider the generalized iterated wreath product Sr1≀…≀SrkS_{r_1}\wr \ldots \wr S_{r_k} of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv admin note: text overlap with arXiv:1409.060
    • …
    corecore