Centralizer (commutant) rings
Finding a basis for the centralizer List of vector space generators for the centralizer ring of \rho(G), written in the basis given by . The matrices are given as a list of blocks. Let G have irreducible representations \rho_i with multiplicities m_i. The centralizer has dimension \sum_i m_i^2 as a \mathbb{C}-vector space. This function gives the minimal number of generators required. List of vector space generators for the centralizer ring of \rho(G). This gives the same result as , but with the matrices given in their entirety: not as lists of blocks, but as full matrices.
Using the centralizer for computations \sum_{s \in t^G} \rho(s), where t is a representative of the conjugacy class class of G. We require that rho is unitary. Uses the given orthonormal basis (with respect to the inner product \langle A, B \rangle = \mbox{Trace}(AB^*)) for the centralizer ring of rho to calculate the sum of the conjugacy class class quickly, i.e. without summing over the class. NOTE: Orthonormality of cent_basis and unitarity of rho are checked. See for a version of this function without checks. The checks are not very expensive, so it is recommended you use the function with checks. The same as , but does not check the basis for orthonormality or the representation for unitarity.