Explicit constructions of unitary transformations between equivalent   irreducible representations
  Irreducible representations (irreps) of a finite group $G$ are equivalent if there exists a similarity transformation between them. In this paper, we describe an explicit algorithm for constructing this transformation between a pair of equivalent irreps, assuming we are given an algorithm to compute the matrix elements of these irreps. Along the way, we derive a generalization of the classical orthogonality relations for matrix elements of irreps of finite groups. We give an explicit form of such unitary matrices for the important case of conjugated Young-Yamanouchi representations, when our group $G$ is symmetric group $S(N)$. 
Marek Mozrzymas, Micha{\l} Studzi\'nski, Micha{\l} Horodecki
math.RT math-ph math.MP quant-ph