A domino tableau-based view on type B Schur-positivity

Over the past years, major attention has been drawn to question of identifying Schur-positive sets, i.e. sets permutations whose associated quasisymmetric function is symmetric and can be written as a non-negative sum Schur functions. The set arc permutations, $\pi$ in $S_n$ such that for any $1\leq j \leq n$, $\{\pi(1),\pi(2),\dots,\pi(j)\}$ an interval $\mathbb{Z}_n$ one most noticeable examples. This paper introduces new type B extension Schur-positivity signed based on Chow's functions generating domino tableaux. As important characteristic, our development compatible with works Solomon regarding descent algebra Coxeter groups. In particular, we design preserving bijections between tableaux show they are indeed Schur-positive.