Remarks on Computing Irreducible Characters

Remarks on Computing Irreducible Characters

0.1. Let G be a connected reductive algebraic group defined over a finite field Fq and let G(Fq) be the finite group of all Fq-rational points of G. We would like to present here a strategy for computing the character table of G(Fq) , under the assumption that p, the characteristic of Fq , is sufficiently large. We can assume that G has a simply connected derived group. Indeed, in the general c...

On the irreducible characters of Camina triples

The Camina triple condition is a generalization of the Camina condition in the theory of finite groups. The irreducible characters of Camina triples have been verified in the some special cases. In this paper, we consider a Camina triple (G,M,N)  and determine the irreducible characters of G in terms of the irreducible characters of M and G/N.  

On Squares of Irreducible Characters

We study the finite groups G with a faithful irreducible character whose square is a linear combination of algebraically conjugate irreducible characters of G. In conclusion, we offer another proof of one theorem of Isaacs-Zisser. There are a few papers treating the finite groups possessing an irreducible character whose powers are linear combinations of appropriate irreducible characters, for ...

On Degrees of Irreducible Brauer Characters

Based on a large amount of examples, which we have checked so far, we conjecture that |G|p′ ≤ ∑ φ φ(1) 2 where p is a prime and the sum runs through the set of irreducible Brauer characters in characteristic p of the finite group G. We prove the conjecture simultaneously for p-solvable groups and groups of Lie type in the defining characteristic. In non-defining characteristics we give asymptot...

On the Irreducible Characters of Hecke Algebras