Geodesic
Ordering families using Lusztig's symbols in type $B$: the integer case
Journal of Algebraic Combinatorics, Tome 41 (2015) no. 1, pp. 157-183.

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

Let $\mathrm{Irr}(W)$ be the set of irreducible representations of a finite Weyl group $W$. Following an idea from Spaltenstein, M. Geck [Comment. Math. Helv. 87, No. 4, 905--927 (2012; Zbl 1264.20005)] has recently introduced a preorder $\preceq_L$ on $\mathrm{Irr}(W)$ in connection with the notion of Lusztig families. In a later paper, M. Geck and L. Iancu [J. Algebr. Comb. 38, No. 2, 457--489 (2013; Zbl 1291.20038)] have shown that in type $B$ (in the asymptotic case and in the equal parameter case) this preorder coincides with the preorder on Lusztig symbols as defined by M. Geck and N. Jacon [Representations of Hecke algebras at roots of unity. Berlin: Springer (2011; Zbl 1232.20008)]. In this paper, we show that this characterisation extends to the so-called integer case, that is, when the ratio of the parameters is an integer.
Classification : 05E10, 20G05, 20F55
Keywords: Lusztig's families, Lusztig's symbols, representation of Weyl groups 
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     author = {Guilhot, J\'er\'emie and Jacon, Nicolas},
     title = {Ordering families using {Lusztig's} symbols in type $B$: the integer case},
     journal = {Journal of Algebraic Combinatorics},
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Guilhot, Jérémie; Jacon, Nicolas. Ordering families using Lusztig's symbols in type $B$: the integer case. Journal of Algebraic Combinatorics, Tome 41 (2015) no. 1, pp. 157-183. http://geodesic.mathdoc.fr/item/JAC_2015__41_1_a2/