We introduce semi-infinite Young tableaux, and show that these tableaux give a combinatorial model for the crystal basis of a level-zero extremal weight module over the quantized universal enveloping algebra of untwisted affine type . The definition and characterization of these tableaux are based on standard monomial theory for semi-infinite Lakshmibai–Seshadri paths and a tableau criterion for the semi-infinite Bruhat order on affine Weyl groups of type , which are also proved in this paper.
Revised: 2020-05-29
Accepted: 2020-06-01
Published online: 2020-10-12
Keywords: Semi-infinite Young tableau, semi-infinite Lakshmibai–Seshadri path, semi-infinite Bruhat order, affine Weyl group, quantum affine algebra, extremal weight module, crystal basis.
@article{ALCO_2020__3_5_1141_0,
author = {Ishii, Motohiro},
title = {Semi-infinite Young tableaux and standard monomial theory for semi-infinite Lakshmibai--Seshadri paths},
journal = {Algebraic Combinatorics},
pages = {1141--1163},
publisher = {MathOA foundation},
volume = {3},
number = {5},
year = {2020},
doi = {10.5802/alco.130},
language = {en},
url = {alco.centre-mersenne.org/item/ALCO_2020__3_5_1141_0/}
}
Ishii, Motohiro. Semi-infinite Young tableaux and standard monomial theory for semi-infinite Lakshmibai–Seshadri paths. Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1141-1163. doi : 10.5802/alco.130. https://alco.centre-mersenne.org/item/ALCO_2020__3_5_1141_0/
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