%0 Journal Article
%T On symmetrization of 6j-symbols and Levin-Wen Hamiltonian
%A Seung-Moon Hong
%J Mathematics
%D 2009
%I arXiv
%X It is known that every ribbon category with unimodality allows symmetrized $6j$-symbols with full tetrahedral symmetries while a spherical category does not in general. We give an explicit counterexample for this, namely the category $\mathcal{E}$. We define the mirror conjugate symmetry of $6j$-symbols instead and show that $6j$-symbols of any unitary spherical category can be normalized to have this property. As an application, we discuss an exactly soluble model on a honeycomb lattice. We prove that the Levin-Wen Hamiltonian is exactly soluble and hermitian on a unitary spherical category.
%U http://arxiv.org/abs/0907.2204v1