The faithfulness of the orthogonal group case of Brauer's representation of the Brauer centralizer algebras restricted to their Temperley–Lieb subalgebras, which was established by Vaughan Jones, is here proved in a new, elementary and self-contained, manner.
['Kosta Došen', 'Zana KovijaniC', 'Zoran Petrić']
A NEW PROOF OF THE FAITHFULNESS OF BRAUER'S REPRESENTATION OF TEMPERLEY–LIEB ALGEBRAS