Lusztig data of Kashiwara-Nakashima tableaux in type D

Abstract

We describe the embedding from the crystal of Kashiwara-Nakashima tableaux in type $D$ of an arbitrary shape into that of $\mathbf{i}$-Lusztig data associated to a family of reduced expressions $\mathbf{i}$ which are compatible with the maximal Levi subalgebra of type $A$. The embedding is described explicitly in terms of well-known combinatorics of type $A$ including the Schützenberger's jeu de taquin and an analog of RSK algorithm.

arXiv comment35 pages, typos corrected, comments added on Remark 5.3 and Remark 5.4, to appear in Algebras and Representation Theory

References in corpus (4)

• Combinatorial descriptions of the crystal structure on certain PBW bases
• RSK correspondence and classically irreducible Kirillov-Reshetikhin crystals
• Super duality and Crystal bases for quantum orthosymplectic superalgebras II
• Quantum nilpotent subalgebras of classical quantum groups and affine crystals

Cited by in corpus (3)

• Unipotent quantum coordinate ring and prefundamental representations for types $A_n^{(1)}$ and $D_n^{(1)}$
• A combinatorial realization of Kirillov-Reshetikhin crystals for type E arising from translations
• Extremal weight crystals over affine Lie algebras of infinite rank