On the irreducible representations of the specializations of the generic Hecke algebra of type \(F_4^*\) (Q1306908)

The aim of this paper is to complete the determination of the irreducible modules of specialized Hecke algebras of type \(F^4\), except over fields of characteristics 2 or 3. The determination of the irreducibles in the case where two parameters are equal has been obtained by Geck and Lux, and many of the other cases have been solved by Bremke. The authors prove that the decomposition matrices may be expressed in lower unitriangular form in all cases, but the argument is a lengthy case by case check rather than a conceptual proof. Full details of the calculations are not given in the paper; the interested reader is invited to contact the authors via email for the details.