The product monomial crystal was defined by Kamnitzer, Tingley, Webster, Weekes, and Yacobi for any semisimple simply-laced Lie algebra , and depends on a collection of parameters . 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 , we show the product monomial crystal is the crystal of a generalised Schur module associated to a column-convex diagram depending on .
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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 = {http://www.numdam.org/articles/10.5802/alco.156/} }
TY - JOUR AU - Gibson, Joel TI - A Demazure Character Formula for the Product Monomial Crystal JO - Algebraic Combinatorics PY - 2021 SP - 301 EP - 327 VL - 4 IS - 2 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.156/ DO - 10.5802/alco.156 LA - en ID - ALCO_2021__4_2_301_0 ER -
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. http://www.numdam.org/articles/10.5802/alco.156/
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