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.
Monodromy in Kazhdan-Lusztig cells in affine type A
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abstract
We use the affine Robinson-Schensted correspondence to describe the structure of bidirected edges in the Kazhdan-Lusztig cells in affine type A. Equivalently, we give a comprehensive description of the Knuth equivalence classes of affine permutations.
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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.