Branching Laws for Polynomial Endomorphisms of Cuntz Algebras Arising from Permutations

Abstract

In our previous article, we have presented a class of endomorphisms of the Cuntz algebras which are defined by polynomials of canonical generators and their conjugates. We showed the classification of some case under unitary equivalence by help of branching laws of permutative representations which are called cycles. In this article, we generalize results not only the cycle case but also the chain case and we give the maximum of the branching number of such branching laws. Further we classify endomorphisms effectively by graphs associated with their branching laws.