A Color-to-Spin Domino Schensted Algorithm

Abstract

We describe the domino Schensted algorithm of Barbasch, Vogan, Garfinkle and van Leeuwen. We place this algorithm in the context of Haiman's mixed and left-right insertion algorithms and extend it to colored words. It follows easily from this description that total color of a colored word maps to the sum of the spins of a pair of $2$-ribbon tableaux. Various other properties of this algorithm are described, including an alternative version of the Littlewood-Richardson bijection which yields the $q$-Littlewood-Richardson coefficients of Carré and Leclerc. The case where the ribbon tableau decomposes into a pair of rectangles is worked out in detail. This case is central in recent work by D. White on the number of even and odd linear extensions of a product of two chains.