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Type A-admissible cells are Kazhdan-Lusztig

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arxiv 1807.07457 v3 pith:RDQ4RMYO submitted 2018-07-19 math.RT math.GR

Van Minh Nguyen This is my paper · ORCID
classification math.RTmath.GR
keywords kazhdan-lusztigw-graphsa-admissibleadmissiblecellsstembridgetheorytype
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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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  1. Two-row $W$-graphs in affine type $A$

    math.CO 2019-08 conditional novelty 7.0 of 10

    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.

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