Geodesic
Vexillary elements in the hyperoctahedral group
Journal of Algebraic Combinatorics, Tome 8 (1998) no. 2, pp. 139-152.

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Summary: In analogy with the symmetric group, we define the vexillary elements in the hyperoctahedral group to be those for which the Stanley symmetric function is a single Schur Q-function. We show that the vexillary elements can be again determined by pattern avoidance conditions. These results can be extended to include the root systems of types A, B, C, and D. Finally, we give an algorithm for multiplication of Schur Q-functions with a superfied Schur function and a method for determining the shape of a vexillary signed permutation using jeu de taquin.
Keywords: vexillary, Stanley symmetric function, reduced word, hyperoctahedral group 
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     title = {Vexillary elements in the hyperoctahedral group},
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Billey, Sara; Kai Lam, Tao. Vexillary elements in the hyperoctahedral group. Journal of Algebraic Combinatorics, Tome 8 (1998) no. 2, pp. 139-152. http://geodesic.mathdoc.fr/item/JAC_1998__8_2_a5/