2009.69: Modular representation theory of blocks with trivial intersection defect groups

2009.69: Jainbei An and Charles W. Eaton (2005) Modular representation theory of blocks with trivial intersection defect groups. Algebras and Representation Theory, 8 (3). pp. 427-448. ISSN 1386-923X

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DOI: 10.1007/s10468-005-8144-5

Abstract

We show that Uno's refinement of the projective conjecture of Dade holds every block whose defect groups intersect trivially modulo the maximal normal p-subgroup. This corresponds to the block having p-local rank one as defined by Jianbei An and Eaton. An immediate consequence is that Dade's projective conjecture, Alperin-McKay conjecture and Puig's nilpotent block conjecture hold for all trivial intersection blocks.

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