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.
Type A-admissible cells are Kazhdan-Lusztig
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abstract
Admissible W-graphs were defined and combinatorially characterised by Stembridge in reference [12]. The theory of admissible W-graphs was motivated by the need to construct W-graphs for Kazhdan-Lusztig cells, which play an important role in the representation theory of Hecke algebras, without computing Kazhdan-Lusztig polynomials. In this paper, we shall show that type A-admissible W-cells are Kazhdan-Lusztig as conjectured by Stembridge in his original paper.
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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.