A Demazure Character Formula for the Product Monomial Crystal
Algebraic Combinatorics, Volume 4 (2021) no. 2, pp. 301-327.

The product monomial crystal was defined by Kamnitzer, Tingley, Webster, Weekes, and Yacobi for any semisimple simply-laced Lie algebra 𝔤, and depends on a collection of parameters R. We show that a family of truncations of this crystal are Demazure crystals, and give a Demazure-type formula for the character of each truncation, and the crystal itself. This character formula shows that the product monomial crystal is the crystal of a generalised Demazure module, as defined by Lakshmibai, Littelmann and Magyar. In type A, we show the product monomial crystal is the crystal of a generalised Schur module associated to a column-convex diagram depending on R.

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DOI: https://doi.org/10.5802/alco.156
Classification: 05E10
Keywords: Monomial crystal, generalised schur module, Demazure crystal.
@article{ALCO_2021__4_2_301_0,
     author = {Gibson, Joel},
     title = {A Demazure Character Formula for the Product Monomial Crystal},
     journal = {Algebraic Combinatorics},
     pages = {301--327},
     publisher = {MathOA foundation},
     volume = {4},
     number = {2},
     year = {2021},
     doi = {10.5802/alco.156},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.156/}
}
Gibson, Joel. A Demazure Character Formula for the Product Monomial Crystal. Algebraic Combinatorics, Volume 4 (2021) no. 2, pp. 301-327. doi : 10.5802/alco.156. https://alco.centre-mersenne.org/articles/10.5802/alco.156/

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