Discrete Math Seminar: Sara Billey

We propose an analog of the Little map for reduced expressions for signed permutations. We show that this map respects the transition equations derived from Chevellay's formula on Schubert classes. We discuss many nice properties of the signed Little map which generalize recent work of Hamaker and Young in type A where they proved Lam's conjecture.   As a key step in this work, we define shifted dual equivalence graphs building on work of Assaf and Haiman and prove they can be characterized by axioms.   These graphs are closely related to both the signed Little map and to the Coxeter-Knuth relations of type B due to Kraskiewicz.
 
This talk is based on joint work with Zach Hamaker, Austin Roberts and Ben Young.