The Field of Values of the Height Zero Characters

2023/04/25 by Navarro, Gabriel, Ruhstorfer, Lucas, Tiep, Pham Huu +1
#20C15 #20D20 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2304.12869

Abstract

We determine what are the fields of values of the irreducible p-height zero characters of all finite groups for p=2; we conjecture what they should be for odd primes, and reduce this statement to a problem on blocks of quasi-simple groups.

Related

• Orders of elements and zeros and heights of characters in a finite group
• Characters of positive height in blocks of finite quasi-simple groups
• The Projective Height Zero Conjecture
• Principal blocks, irreducible restriction, fields and degrees
• Groups with small multiplicities of fields of values of irreducible characters