  C. Bonnaf{\'e}, M. Geck, L. Iancu, and T. Lam have conjectured a description
of one-sided cells in unequal parameter Hecke algebras of type $B$ which is
based on domino tableaux of arbitrary rank. In the integer case, this
generalizes the work of D. Garfinkle whose methods we adapt to construct a
family of operators which generate the conjectured combinatorial description.
