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.

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

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