A crystal structure on shifted tableaux, with applications to type B Schubert curves

We present a new crystal-like structure on shifted (marked) semistandard skew tableaux. The raising and lowering operators commute with jeu de taquin slides, and detect the type B Littlewood-Richardson condition as the highest weight entries. Certain substructures satisfy the Kashiwara crystal axioms for the root system of ${GL}_n$. If time permits, we will discuss applications of our new operators to Schubert curves in the orthogonal Grassmannian.

This is joint work with Jake Levinson and Kevin Purbhoo.