1,108 research outputs found
Some remarks on orbital digraphs for the finite primitive groups
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
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
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
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
. 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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