We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the ...

We show that the distribution of symmetry of a naturally reductive nilpotent Lie group coincides with the invariant distribution induced by the set of fixed vectors of the isotropy. This extends a known result on compact ...

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm ...

We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally ...

We analyse some PT-symmetric oscillators with Td symmetry that depend on a potential parameter g. We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of g. Pairs ...

We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive ...

We discuss space-time symmetric Hamiltonian operators of the form H = H0 + igH ′ , where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H ′ is invariant under transformation ...

In this paper, we deal with reversing and extended symmetries of subshifts generated by bijective substitutions. We survey some general algebraic and dynamical properties of these subshifts and recall known results regarding ...

The centralizer (automorphism group) and normalizer (extended symmetry group) of the shift action inside the group of self-homeomorphisms are studied, in the context of certain Z(d) subshifts with a hierarchical supertile ...