A note on the Glauberman correspondence

ABSTRACT

In this paper, we will investigate the Glauberman-Watanabe correspondence between the characters and blocks. Motivated by the work of Puig and Zhou [10] which is about the extension of a nilpotent block and its Glauberman correspondent, we will modify the basic Morita equivalence obtained in their work and get a new equivalence such that the correspondence between characters induced by this equivalence coincides with the Glauberman correspondence under the situation that the block is a p-extension of a nilpotent block.

KEYWORDS:

• Glauberman correspondence
• Morita equivalence
• nilpotent blocks

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20C15