A note on the Glauberman-Watanabe corresponding blocks of finite groups with normal defect groups. (English) Zbl 1202.20014
Author’s summary: Harris proved that there is an indecomposable bimodule with a trivial source which induces a Morita equivalence between Glauberman-Watanabe corresponding block algebras of finite groups with normal defect groups and the Glauberman correspondence of characters in corresponding blocks. We note an implication of the Puig correspondence in the context of the Glauberman-Watanabe correspondence and then, using this, show Harris’s theorem in two ways.
Reviewer: Morten E. Harris (Chicago)
MSC:
| 20C20 | Modular representations and characters |
| 20C05 | Group rings of finite groups and their modules (group-theoretic aspects) |
Keywords:
Glauberman correspondence; Watanabe correspondence; perfect isometries; isotypies; character correspondences; blocks; finite groups; irreducible characters; defect groupsReferences:
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