Combinatorics Seminar: A crystal-like structure on shifted tableaux

Seminar | March 12 | 12-1 p.m. | 939 Evans Hall

 Maria Monks Gillespie, UC Davis

 Department of Mathematics

We establish a crystal-like structure on shifted tableaux, whose characters are the Schur $Q$-functions. In particular, we will define two sets of coplactic raising and lowering operators $E$, $F$, $E'$, and $F'$ on shifted tableaux that each independently give a type A Kashiwara crystal. Taken together, these operators detect highest weight skew shifted tableaux, giving a new shifted Littlewood-Richardson rule. We also give local axioms that characterize these "doubled crystals", analogous to Stembridge's axioms for ordinary tableaux crystals.

If time permits, we will discuss some applications of these operators to understanding real Schubert curves in the orthogonal Grassmannian. This is joint work with Jake Levinson and Kevin Purbhoo.