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Type B plactic relations for $r$-domino tableaux

Abstract : The recent work of Bonnafé et al. (2007) 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 given two signed permutations have the same insertion $r$-domino tableaux in Garfinkle's algorithm (1990). 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 tool for their proofs.
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Müge Taşkin. Type B plactic relations for $r$-domino tableaux. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.833-846, ⟨10.46298/dmtcs.2700⟩. ⟨hal-01185392⟩

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