On the Inductive Alperin-McKay Conditions in the Maximally Split Case

2020/08/23 by Cabanes, Marc, Fry, A. A. Schaeffer, Späth, Britta
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2008.10096

Abstract

The Alperin-McKay conjecture relates height zero characters of an ℓ-block with the ones of its Brauer correspondent. This conjecture has been reduced to the so-called inductive Alperin-McKay conditions about quasi-simple groups by the third author. Those conditions are still open for groups of Lie type. The present paper describes characters of height zero in ℓ-blocks of groups of Lie type over a field with q elements when ℓ divides q-1. We also give information about ℓ-blocks and Brauer correspondents. As an application we show that quasi-simple groups of type C over \mathbbF_q satisfy the inductive Alperin-McKay conditions for primes ℓ≥ 5 and dividing q-1. Some methods to that end are adapted from the work of Malle--Späth.

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