Geodesic
Demazure crystals for flagged key polynomials
Jiayi Wen1
1The Hong Kong University of Science and Technology
The electronic journal of combinatorics, Tome 32 (2025) no. 1

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Zbl DOI arXiv
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.
DOI : 10.37236/13127
Classification : 05E10, 05E05
Mots-clés : key tableaux, Morse-Schilling crystals

Jiayi Wen  1

1 The Hong Kong University of Science and Technology 
Jiayi Wen. Demazure crystals for flagged key polynomials. The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/13127
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     author = {Jiayi Wen},
     title = {Demazure crystals for flagged key polynomials},
     journal = {The electronic journal of combinatorics},
     year = {2025},
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     number = {1},
     doi = {10.37236/13127},
     zbl = {1564.05366},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/13127/}
}
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