Rationality of blocks of quasi-simple finite groups

2018/05/05 by Farrell, Niamh, Kessar, Radha
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1805.02015

Abstract

Let ℓ be a prime number. We show that the Morita Frobenius number of an ℓ-block of a quasi-simple finite group is at most 4 and that the strong Frobenius number is at most 4|D|²!, where D denotes a defect group of the block. We deduce that a basic algebra of any block of the group algebra of a quasi-simple finite group over an algebraically closed field of characteristic ℓ is defined over a field with ℓ^a elements for some a ≤ 4. We derive consequences for Donovan's conjecture. In particular, we show that Donovan's conjecture holds for ℓ-blocks of special linear groups.

Related

• Donovan's conjecture, blocks with abelian defect groups and discrete valuation rings
• Towards Donovan's conjecture for abelian defect groups
• Arbitrarily large Morita Frobenius numbers
• The strong Frobenius numbers for cyclic defect blocks are equal to one
• On the number of characters in blocks of quasi-simple groups