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Journal Articles Journal of Algebraic Combinatorics Year : 2015

Ordering Families using Lusztig's symbols in type B: the integer case

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Abstract

Let $\Irr(W)$ be the set of irreducible representations of a finite Weyl group $W$. Following an idea from Spaltenstein, Geck has recently introduced a preorder $\leq_L$ on $\Irr(W)$ in connection with the notion of Lusztig families. In a later paper with Iancu, they have shown that in type $B$ (in the asymptotic case and in the equal parameter case) this order coincides with the order on Lusztig symbols as defined by Geck and the second author in \cite{GJ}. In this paper, we show that this caracterisation extends to the so-called integer case, that is when the ratio of the parameters is an integer.

Dates and versions

hal-00857874 , version 1 (04-09-2013)

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Jeremie Guilhot, Nicolas Jacon. Ordering Families using Lusztig's symbols in type B: the integer case. Journal of Algebraic Combinatorics, 2015, 41 (1), pp.157-183. ⟨10.1007/s10801-014-0531-8⟩. ⟨hal-00857874⟩
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