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arXiv · 2309.17025

Demazure crystals for flagged key polynomials

Jiayi Wen
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Abstract

One definition of key polynomials is as the weight generating functions of key tableaux. Assaf and Schilling introduced a crystal structure on key tableaux and related it to Morse--Schilling crystals on reduced factorizations for permutations via weak Edelman--Greene insertion. In this paper, we consider generalizations of both crystals depending on a flag. We extend weak EG insertion to a bijection between our flagged objects and show that the recording tableau gives a crystal isomorphism. As an application, we show that flagged key tableaux have a natural Demazure crystal structure, whose characters recover Reiner and Shimozono's flagged key polynomials.

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Jiayi Wen. 2024-06-17. Demazure crystals for flagged key polynomials. https://arxiv.org/abs/2309.17025

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