Abstract
We compute matrix units for Brauer's centralizer algebras and Hecke algebras of type A. This can be used to construct a complete system of matrix units of the centralizers of tensor products of classical Lie groups (except SO(2n)) and their quantum deformations. The calculation is done by induction inspired by path models for special operator algebras. It is similar to the calculation of Young's orthogonal matrix units for the symmetric group as given by Rutherford.
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