A Major-Index Preserving Map on Fillings

Per Alexandersson, Mehtaab Sawhney

Abstract


We generalize a map by S. Mason regarding two combinatorial models for key polynomials, in a way that accounts for the major index. Furthermore we define a similar variant of this map, that regards alternative models for the modified Macdonald polynomials at t=0, and thus partially answers a question by J. Haglund. These maps together imply a certain uniqueness property regarding inversion–and coinversion-free fillings. These uniqueness properties allow us to generalize the notion of charge to a non-symmetric setting, thus answering a question by A. Lascoux and the analogous question in the symmetric setting proves a conjecture by K. Nelson.

Keywords


Macdonald polynomials; Hall–Littlewood polynomials; Charge; Major index; Demazure characters; Key polynomials

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