Semi-infinite Young tableaux and standard monomial theory for semi-infinite Lakshmibai–Seshadri paths
Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1141-1163.

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 A. 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 A, which are also proved in this paper.

Received: 2019-09-30
Revised: 2020-05-29
Accepted: 2020-06-01
Published online: 2020-10-12
DOI: https://doi.org/10.5802/alco.130
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},
     publisher = {MathOA foundation},
     volume = {3},
     number = {5},
     year = {2020},
     pages = {1141-1163},
     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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