1,108 research outputs found

    Some remarks on orbital digraphs for the finite primitive groups

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    In this paper we concern with the relationship between the finite groups PSL(2, q), q>5 a prime, and orbital digraphs. And also we explain that for a generator elliptic element in permutation group, there is a hyperbolic circuit in suborbital graph

    A comment on the bianchi groups

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    In this paper, we aim to discuss several the basic arithmetic structure of Bianchi groups. In particularly, we study fundamental domain and directed orbital graphs for the group PSL(2;O_1)

    The kinematical Hilbert space of Loop Quantum Gravity from BF theories

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    In this work, it is demonstrated how the kinematical Hilbert space of Loop Quantum Gravity (LQG) can be inferred from the configuration space of BF theories via the imposition of the Hamiltonian constraints. In particular, it is outlined how the projection to the representations associated with Ashtekar-Barbero connections provides the correct procedure to implement second-class constraints and the corresponding nontrivial induced symplectic structure. Then, the reduction to SU(2) invariant intertwiners is analyzed and the properties of LQG states under Lorentz transformations is discussed.Comment: 13 page

    Orbit counting in conjugacy classes for free groups acting on trees

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    In this paper we study the action of the fundamental group of a finite metric graph on its universal covering tree. We assume the graph is finite, connected and the degree of each vertex is at least three. Further, we assume an irrationality condition on the edge lengths. We obtain an asymptotic for the number of elements in a fixed conjugacy class for which the associated displacement of a given base vertex in the universal covering tree is at most TT. Under a mild extra assumption we also obtain a polynomial error term.Comment: 13 pages, additional section discusses error terms, revised expositio
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