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RSK bases and Kazhdan-Lusztig cells

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arxiv 0902.2842 v3 pith:3PY45STW submitted 2009-02-17 math.RT math.CO

K. N. Raghavan , Preena Samuel , K. V. Subrahmanyam This is my paper · ORCID
classification math.RTmath.CO
keywords groupbasescellskazhdan-lusztigsymmetrictheorytwo-sidedalgebra
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From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, 'RSK bases' are constructed for certain quotients by two-sided ideals of the group ring and the Hecke algebra. Applications to invariant theory, over various base rings, of the general linear group and representation theory of the symmetric group are discussed.

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  1. Rook sums in the symmetric group algebra

    math.CO 2025-07 conditional novelty 6.0 of 10

    Rook sums in the symmetric group algebra satisfy an explicit product rule, have linearly factorable minimal polynomials, and generate ideals whose sizes count pattern-avoiding permutations.

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