A finite tensor category is called pointed if all its simple objects are invertible. We find necessary and sufficient conditions for two pointed semisimple categories to be dual to each other with respect to a module category. Whenever the dual of a pointed semisimple category with respect to a module category is pointed, we give explicit formulas for the Grothendieck ring and for the associato...

We argue that the classical description of a symplectic manifold endowed with a Hamiltonian action of an abelian Lie group G and the corresponding quantum theory can be understood as different aspects of the unitary representation theory of G. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry (notably, Souriau’s moment map and the Mardsen-Weinstein sympl...

Latent symmetry of a component of a composite object is defined as that symmetry of a subunit of the component which is not a symmetry of the component but which is a symmetry of the composite. This is illustrated by a geometrical example. A group theoretical procedure is given to determine latent symmetry and is applied to examples.

In two-parameter systems two symmetry breaking bi-furcation points of diierent types coalesce generically within one point. This causes secondary bifurcation points to exist. The aim of this paper is to understand this phenomenon with group theory and the innerconnectivity of irreducible representations of super-group and subgroups. Colored pictures of examples are included.

The classification of polarization elements, the polarization affecting optical devices which have a Jones-matrix representation, according to the type of eigenvectors they possess, is given a new visit through the Group-Theoretical connection of polarization elements. The diattenuators and retarders are recognized as the elements corresponding to boosts and rotations, respectively. The structu...

The purpose of this paper is to obtain the tracking interval for difference of expected Kullback-Leibler risks of two models under Type II hybrid censoring scheme. This interval helps us to evaluate proposed models in comparison with each other. We drive a statistic which tracks the difference of expected Kullback–Leibler risks between maximum likelihood estimators of the distribution in two diff...