Massachusetts Institute of Technology SPUR

Authors Yu. I. Manin and V. V. Schechtman developed the theory of “higher Bruhat orders,” presenting a family of combinatorial objects closely related to the symmetric group. In particular, the two authors define a series of ranked posets which generalize the weak left Bruhat order; their construction has found applications in geometry and representation theory. In this paper, we define a similar combinatorial system for the group Bn of hypercube symmetries. We prove the analogue of Manin and Schechtman’s theorem for the cases k = 1 and k = 2, and relate these orders to the structure of the group Bn. Suggested by Ben Elias