# zbMATH — the first resource for mathematics

Brauer trees for the Schur cover of the symmetric group. (English) Zbl 1068.20016
Brauer trees of the faithful blocks of weight $$1$$ of the Schur double covers of the symmetric group $$S_n$$ and the alternating group $$A_n$$ in odd characteristic are determined. As a corollary, faithful blocks of weight 1 of $$\widetilde S_n$$ are classified up to Morita equivalence – there are $$\lfloor(p+3)/4\rfloor$$ such equivalence classes (whereas for a fixed $$p$$ there is only one such equivalence class for $$S_n$$).

##### MSC:
 20C30 Representations of finite symmetric groups 20C20 Modular representations and characters
##### Keywords:
Brauer trees; Schur covers; symmetric groups; alternating groups
GAP
Full Text:
##### References:
 [1] Alperin, J., Local representation theory, Cambridge stud. adv. math., 11, (1986), Cambridge Univ. Press Cambridge · Zbl 0593.20003 [2] Beyl, F.; Tappe, J., Group extensions, representations and the Schur multiplicator, Lecture notes in math., 958, (1982), Springer New York · Zbl 0544.20001 [3] Cabanes, M., Local structure of the p-blocks of $$Sn$$, Math. Z., 198, 519-543, (1988) · Zbl 0646.20011 [4] Feit, W., The representation theory of finite groups, (1982), North-Holland Amsterdam · Zbl 0493.20007 [5] Feit, W., Possible Brauer trees, Illinois J. math., 18, 1, 43-56, (1984) · Zbl 0538.20006 [6] GAP—groups, algorithms, and programming, version 4.2, (2000), Aachen St. Andrews [7] Goldschmidt, D., Lectures on character theory, (1980), Publish or Perish Berkeley · Zbl 0433.20006 [8] Hiss, G.; Lux, K., Brauer trees of sporadic groups, (1989), Clarendon Oxford · Zbl 0685.20013 [9] Hoffman, P.; Humphreys, J., Projective representations of the symmetric groups, (1992), Clarendon Oxford · Zbl 0777.20005 [10] Humphreys, J., Blocks of projective representations of the symmetric groups, J. London math. soc., 33, 2, 441-452, (1986) · Zbl 0633.20007 [11] James, G.; Kerber, A., The representation theory of the symmetric group, Encyclopedia math., 16, (1981), Addison-Wesley Reading, MA [12] Kessar, R., Blocks and source algebras for the double covers of the symmetric and alternating groups, J. algebra, 186, 872-933, (1996) · Zbl 0894.20015 [13] Morris, A., The spin representation of the symmetric group, Canad. J. math., 17, 543-549, (1965) · Zbl 0135.05602 [14] Noeske, F., Zur darstellungstheorie der schurschen erweiterungen symmetrischer gruppen, (2002), Diplomarbeit RWTH Aachen [15] Schur, I., Über die darstellung der symmetrischen und der alterniereden gruppe durch gebrochen lineare substitutionen, J. reine angew. math., 139, 155-250, (1911) · JFM 42.0154.02
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.