The decomposition numbers of the hecke algebra of type F₄

Let W be the finite Coxeter group of type F₄, and H_rq be the associated Hecke algebra, with parameter a prime power q, defined over a valuation ring R in a large enough extension field of Q, with residue class field of characteristic r. In this paper, the r-modular decomposition numbers of H_Rq are determined for all q and r such that r does not divide q. The methods of the proofs involve the study of the generic Hecke algebra of type F₄ over the ring A = ℤ[u^1/2, u^-1/2] of Laurent polynomials in an indeterminate u^1/2 and its specializations onto the ring of integers in various cyclotomic number fields. Substancial use of computers and computer program systems (GAP, MAPLE, Meat-Axe) has been made.