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

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.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00857874
Contributor : Jeremie Guilhot <>
Submitted on : Wednesday, September 4, 2013 - 10:35:38 AM
Last modification on : Thursday, January 30, 2020 - 3:54:05 PM

### Identifiers

• HAL Id : hal-00857874, version 1
• ARXIV : 1308.3945

### Citation

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

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