We check the McKay conjecture on character degrees for the case of symplectic groups over the field with two elements and the prime 2. Then we check the inductive McKay condition (Isaacs–Malle–Navarro) for and all primes.
Nous vérifions la conjecture de McKay sur les degrés de caractères dans le cas des groupes symplectiques sur le corps à deux éléments et du nombre premier 2. Nous montrons ensuite la condition de McKay inductive (Isaacs–Malle–Navarro) pour et tous les nombres premiers.
Accepted:
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Marc Cabanes 1
@article{CRMATH_2011__349_11-12_611_0, author = {Marc Cabanes}, title = {Odd character degrees for $ \mathrm{Sp}(2n,2)$}, journal = {Comptes Rendus. Math\'ematique}, pages = {611--614}, publisher = {Elsevier}, volume = {349}, number = {11-12}, year = {2011}, doi = {10.1016/j.crma.2011.05.007}, language = {en}, }
Marc Cabanes. Odd character degrees for $ \mathrm{Sp}(2n,2)$. Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 611-614. doi : 10.1016/j.crma.2011.05.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.05.007/
[1] On the inductive McKay condition in the defining characteristic, Math. Z., Volume 263 (2009) no. 2, pp. 411-424
[2] M. Cabanes, B. Späth, Equivariance and extendibility in finite reductive groups with connected center, in preparation, 2011.
[3] Simple Groups of Lie Type, Wiley, New York, 1972
[4] Representations of Finite Groups of Lie Type, Cambridge University Press, 1991
[5] The Classification of the Finite Simple Groups, Math. Surveys Monogr., vol. 3, Amer. Math. Soc., Providence, 1998
[6] On the degrees of Steinberg characters of Chevalley groups, Math. Z., Volume 135 (1974), pp. 125-135
[7] A reduction theorem for McKay conjecture, Invent. Math., Volume 170 (2007), pp. 33-101
[8] Irreducible representations of finite classical groups, Invent. Math., Volume 43 (1977), pp. 125-175
[9] Height 0 characters of finite groups of Lie type, Represent. Theory, Volume 11 (2007), pp. 192-220
[10] The inductive McKay condition for simple groups not of Lie type, Comm. Algebra, Volume 36 (2008) no. 2, pp. 455-463
[11] Sylow d-tori of classical groups and the McKay conjecture I, J. Algebra, Volume 323 (2010), pp. 2469-2493
[12] Sylow d-tori of classical groups and the McKay conjecture II, J. Algebra, Volume 323 (2010), pp. 2494-2509
[13] Inductive McKay condition in defining characteristic, 2010 (preprint) | arXiv
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