Geodesic
Plactic relations for \(r\)-domino tableaux
The electronic journal of combinatorics, Tome 19 (2012) no. 1
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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.
DOI : 10.37236/2042
Classification : 05E10
Mots-clés : Kazhdan-Lusztig theory, Garfinkle's equivalence relation 
@article{10_37236_2042,
     author = {M\"uge Ta\c{s}kin},
     title = {Plactic relations for \(r\)-domino tableaux},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {1},
     doi = {10.37236/2042},
     zbl = {1244.05231},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2042/}
}
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Müge Taşkin. Plactic relations for \(r\)-domino tableaux. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/2042

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