A Type B Analogue to Ribbon Tableaux

We introduce a shifted analogue of the ribbon tableaux defined by James and Kerber. For any positive integer $k$, we give a bijection between the $k$-ribbon fillings of a shifted shape and regular fillings of a $\lfloor k/2\rfloor$-tupleofshapescalledits$k$-quotient. We also define the corresponding generating functions, and prove that they are symmetric, Schur positive and Schur $Q$-positive.