ALGEBRAIC COMBINATORICS

no. 5
Semi-infinite Young tableaux and standard monomial theory for semi-infinite Lakshmibai–Seshadri paths
Ishii, Motohiro1
1 Department of Mathematics Cooperative Faculty of Education Gunma University Maebashi Gunma 371-8510 Japan
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:
Revised:
Accepted:
Published online:
DOI: 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.
Ishii, Motohiro 1

1 Department of Mathematics Cooperative Faculty of Education Gunma University Maebashi Gunma 371-8510 Japan 
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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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