Two-row shapes in affine type A admit finite W-graphs, constructed combinatorially and proven unique up to isomorphism, extending the known finite-type picture.
An affine generalization of evacuation
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abstract
We establish the existence of an involution on tabloids that is analogous to Schutzenberger's evacuation map on standard Young tableaux. We find that the number of its fixed points is given by evaluating a certain Green's polynomial at $q = -1$, and satisfies a "domino-like" recurrence relation.
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Two-row $W$-graphs in affine type $A$
Two-row shapes in affine type A admit finite W-graphs, constructed combinatorially and proven unique up to isomorphism, extending the known finite-type picture.