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

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.

preprint2020arXivOpen access
William M. McGovern
math.COmath.RT
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William M. McGovern

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