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.
Bibliographical noteFunding Information:
M.C. was partially supported by NSF Grant DMS-1503119. J.B.L. was partially supported by NSF Grant DMS-1401792. P.P. was partially supported by NSF Grants DMS-1148634, DMS-1351590, and a Sloan Fellowship.
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