On the Irreducible Representations of the Specializations in Characteristics 2 and 3 of the Generic Hecke Algebra of Type F4

Abstract

A complete determination of the irreducible modules of specialized Hecke algebras of type F 4 , with respect to specializations with equal parameters, has been obtained by M. Geck and K. Lux (1991, Manuscripta Math. 70, 285-306) for all characteristics. A similar determination for specializations with v = u 2 and v = u 4 has been obtained by K. Bremke (1994, Manuscripta Math. 83, 331-346). In another paper (1999, J. Algebra, 218, 654-671), the authors determined 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. In this paper, the corresponding results for characteristic 2 or 3 are obtained. Again, it is found that the decomposition matrices may be expressed in lower uni-triangular form in all these cases and that the splitting fields are those generated by the images of the parameters.