On the Irreducible Representations of the Specializations of the Generic Hecke Algebra of Type F4,

A complete determination of the irreducible modules of specialized Hecke algebras of type F4, with respect to specializations with equal parameters, was obtained by M. Geck and K. Lux (1991, Manuscripta Math.70, 285–306). A similar determination for specializations with v = u2 and v = u4 was obtained by K. Bremke (1994, Manuscripta Math.83, 331–346). In this paper, we determine the irreducible modules for all remaining specializations other than those into fields of characteristic 2 or 3, obtaining en route decompositions of the generic irreducible modules under such specializations. We find that the decomposition matrices may be expressed in lower uni-triangular form in all these cases.