COXETER-KNUTH GRAPHS AND A SIGNED LITTLE MAP FOR TYPE B REDUCED WORDS

Abstract. We define an analog of David Little’s algorithm for reduced words in type B, and investigate its main properties. In particular, we show that our algo-rithm preserves the recording tableaux of Kraśkiewicz insertion, and that it provides a bijective realization of the type B transition equations in Schubert calculus. Many other aspects of type A theory carry over to this new setting. Our primary tool is a shifted version of the dual equivalence graphs defined by Assaf and further developed by Roberts. We provide an axiomatic characterization of shifted dual equivalence graphs, and use them to prove a structure theorem for the graph of type B Coxeter-Knuth relations. 1