Transition operators

In this paper, we give a generic algorithm of the transition operators between Hermitian Young projection operators corresponding to equivalent irreducible representations of ????????(N), using the compact expressions of Hermitian Young projection operators derived in the work of Alcock-Zeilinger and Weigert [eprint arXiv:1610.10088 [math-ph]]. We show that the Hermitian Young projection operators together with their transition operators constitute a fully orthogonal basis for the algebra of invariants of V⊗m that exhibits a systematically simplified multiplication table. We discuss the full algebra of invariants over V⊗3 and V⊗4 as explicit examples. In our presentation, we make use of various standard concepts, such as Young projection operators, Clebsch-Gordan operators, and invariants (in birdtrack notation). We tie these perspectives together and use them to shed light on each other.