Canonical bases for the Brauer centralizer algebra (Q1902198)

The authors construct canonical bases for the Birman-Wenzl algebra \(BW_n\), the \(q\)-analogue of the Brauer centralizer algebra, and so define left, right and two-sided cells. They describe these objects combinatorially and show that each left cell carries an irreducible representation of \(BW_n\). In particular, they obtain canonical bases for each representation, defined over \(\mathbb{Z}\), and show that every representation is induced from a representation of a symmetric group in a precise way.