Decomposition numbers for the principal Φ 2n -block of Sp 4n (q) and SO 4n+1 (q)
[Nombres de décomposition pour le bloc principal Φ 2n de Sp 4n (q) et SO 4n+1 (q)]
Dudas, Olivier1 ; Norton, Emily2
1 Aix-Marseille Université, CNRS, Institut de Mathématiques de Marseille – I2M Campus de Luminy, Avenue de Luminy, Case 930, 13288 Marseille Cedex 9 (France)
2 School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent, CT2 7NZ (United Kingdom)
Annales de l'Institut Fourier, Online first, 44 p.

Nous calculons les nombres de décomposition des caractères unipotents du ℓ-bloc unipotent d’un groupe fini de type de Lie B 2n (q) ou C 2n (q) lorsque q est une puissance d’un nombre premier impair et ℓ est un nombre premier impair avec q d’ordre 2n dans 𝔽 ℓ . En cours de route, nous étendons à ces groupes finis les résultats de [12] sur le graphe de branchement pour l’induction et la restriction de Harish-Chandra.

We compute the decomposition numbers of the unipotent characters lying in the principal ℓ-block of a finite group of Lie type B 2n (q) or C 2n (q) when q is an odd prime power and ℓ is an odd prime number such that the order of q mod ℓ is 2n. Along the way, we extend to these finite groups the results of [12] on the branching graph for Harish-Chandra induction and restriction.

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DOI : 10.5802/aif.3659
Classification : 20C20, 20C33
Keywords: Finite groups of Lie type, Decomposition numbers.
Mot clés : Groupes finis de type Lie, nombres de décomposition.
Dudas, Olivier 1 ; Norton, Emily 2

1 Aix-Marseille Université, CNRS, Institut de Mathématiques de Marseille – I2M Campus de Luminy, Avenue de Luminy, Case 930, 13288 Marseille Cedex 9 (France)
2 School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent, CT2 7NZ (United Kingdom) 
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     title = {Decomposition numbers for the principal $\Phi _{2n}$-block of $\mathrm{Sp}_{4n}(q)$ and $\mathrm{SO}_{4n+1}(q)$},
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Dudas, Olivier; Norton, Emily. Decomposition numbers for the principal $\Phi _{2n}$-block of $\mathrm{Sp}_{4n}(q)$ and $\mathrm{SO}_{4n+1}(q)$. Annales de l'Institut Fourier, Online first, 44 p.

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