Geodesic
Equivalence classes in the Weyl groups of type $B_n$.
Journal of Algebraic Combinatorics, Tome 27 (2008) no. 2, pp. 247-262.

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Summary: We consider two families of equivalence classes in the Weyl groups of type $B _{ n }$ which are suggested by the study of left cells in unequal parameter Iwahori-Hecke algebras. Both families are indexed by a non-negative integer $r$. It has been shown that the first family coincides with left cells corresponding to the equal parameter Iwahori-Hecke algebra when $r=0$; the equivalence classes in the second family agree with left cells corresponding to a special class of choices of unequal parameters when $r$ is sufficiently large. Our main result shows that the two families of equivalence classes coincide, suggesting the structure of left cells for remaining choices of the Iwahori-Hecke algebra parameters.
Classification : 20C08, 05E10
Keywords: keywords unequal parameter iwahori-Hecke algebra, domino tableaux, Robinson-Schensted algorithm 
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     author = {Pietraho, Thomas},
     title = {Equivalence classes in the {Weyl} groups of type $B_n$.},
     journal = {Journal of Algebraic Combinatorics},
     pages = {247--262},
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     volume = {27},
     number = {2},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2008__27_2_a0/}
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Pietraho, Thomas. Equivalence classes in the Weyl groups of type $B_n$.. Journal of Algebraic Combinatorics, Tome 27 (2008) no. 2, pp. 247-262. http://geodesic.mathdoc.fr/item/JAC_2008__27_2_a0/