Plactic relations for $r$-domino tableaux

Müge Taşkin

Abstract


The work of C. Bonnafé, M.Geck, L. Iancu and T. Lam shows through two conjectures that $r$-domino tableaux have an important role in Kazhdan-Lusztig theory of type $B$ with unequal parameters. In this paper we provide plactic relations on signed permutations which determine whether two given signed permutations have the same insertion $r$-domino tableaux in Garfinkle's algorithm. Moreover, we show that a particular extension of these relations can describe Garfinkle's equivalence relation on $r$-domino tableaux which is given through the notion of open cycles. With these results we enunciate the conjectures of Bonnafé et al. and provide necessary tools for their proofs.

Full Text: PDF