The Robinson--Schensted correspondence between the symmetric group and pairs of standard young tableaux gives rise for a way to compute cells of Coxeter groups of type A. A lesser known correspondence exists for signed permutation and pairs of so-called domino tableaux, which allows us to compute cells in Coxeter groups of type D. This talk will describe the computation of these cells and will explore applications to Kazhdan--Lusztig theory.
Domino Tableaux and Cells of Coxeter Groups