Geodesic
Ordering Lusztig's families in type $B _{n }$
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 2, pp. 457-489.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let W be a finite Coxeter group and L be a weight function on W in the sense of Lusztig. We have recently introduced a pre-order relation ?$_{ L }$ on the set of irreducible characters of W which extends Lusztig's definition of "families" and which, conjecturally, corresponds to the ordering given by Kazhdan-Lusztig cells. Here, we give an explicit description of ?$_{ L }$ for W of type B $_{ n }$ and any L. (All other cases are known from previous work.) This crucially relies on some new combinatorial constructions around Lusztig's "symbols". Combined with previous work, we deduce general compatibility results between ?$_{ L }$ and Lusztig's a-function, valid for any W,L.
Keywords: Coxeter groups, Lusztig families, bipartitions and symbols 
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     author = {Geck, Meinolf and Iancu, Lacrimioara},
     title = {Ordering {Lusztig's} families in type $B _{n }$},
     journal = {Journal of Algebraic Combinatorics},
     pages = {457--489},
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     year = {2013},
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Geck, Meinolf; Iancu, Lacrimioara. Ordering Lusztig's families in type $B _{n }$. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 2, pp. 457-489. http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a1/