The decomposition numbers of Hecke algebras of typeF 4 with unequal parameters

Abstract

The purpose of this paper is to calculate the decomposition numbers for Hecke algebras of typeF4 (andC3) with unequal parameters. The problem is reduced to specifying decomposition maps of the generic Hecke algebras. The concept of Kazhdan-Lusztig polynomials and left cells serves to determine their irreducible representations. We also prove a result about the minimal ring over which the irreducible representations of the generic algebras can be realized.