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We exhibit a set of operators on pairs of domino tableaux of the same shapesending them to other such pairs with the same right tableau, in such a waythat any two pairs with the same right tableau are conjugate by somecomposition of the operators. Using these operators we give explicit bases forthe isotypic components of a classical Kazhdan-Lusztig left cell in terms ofKazhdan-Lusztig basis vectors.

A family of operators generating domino tableaux of a fixed shape and a decomposition of left cells into isotypic components