Plactic relations for $r$-domino tableaux

Details Plactic relations for $r$-domino tableaux Plactic relations for $r$-domino tableaux

2008-03-07

arxiv.org/abs/0803.1148v3

Mathematics

Representation Theory

17 pages, 12 figures

Scientific paper

The work of C. Bonnaf{\'e}, M. Geck, L. Iancu and T. Lam \cite{Geck-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 given two signed permutations have the same insertion $r$-domino tableaux in Garfinkle's algorithm \cite{Garfinkle1}.

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