Semi-infinite Young tableaux and standard monomial theory for semi-infinite Lakshmibai–Seshadri paths

Ishii, Motohiro

Algebraic Combinatorics, Tome 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.

Mots-clés : 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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