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.
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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.
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@article{ALCO_2020__3_5_1141_0, author = {Ishii, Motohiro}, title = {Semi-infinite {Young} tableaux and standard monomial theory for semi-infinite {Lakshmibai{\textendash}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 = {https://alco.centre-mersenne.org/articles/10.5802/alco.130/} }
TY - JOUR TI - Semi-infinite Young tableaux and standard monomial theory for semi-infinite Lakshmibai–Seshadri paths JO - Algebraic Combinatorics PY - 2020 DA - 2020/// SP - 1141 EP - 1163 VL - 3 IS - 5 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.130/ UR - https://doi.org/10.5802/alco.130 DO - 10.5802/alco.130 LA - en ID - ALCO_2020__3_5_1141_0 ER -
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/articles/10.5802/alco.130/
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