  We exhibit a set of operators on pairs of domino tableaux of the same shape
sending them to other such pairs with the same right tableau, in such a way
that any two pairs with the same right tableau are conjugate by some
composition of the operators. Using these operators we give explicit bases for
the isotypic components of a classical Kazhdan-Lusztig left cell in terms of
Kazhdan-Lusztig basis vectors.
