Brauer trees for the Schur cover of the symmetric group. (English) Zbl 1068.20016

Müller, Jürgen

J. Algebra 266, No. 2, 427-445 (2003).

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 \(S_n\)).

Reviewer: Pham Huu Tiep (Gainesville)

MSC:

20C30	Representations of finite symmetric groups
20C20	Modular representations and characters

Keywords:

Brauer trees; Schur covers; symmetric groups; alternating groups

Software:

GAP

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