HECKE ALGEBRAS OF TYPE-A WITH Q=-1

In this paper we study the decomposition matrices of the Hecke algebra s of type A with q = -1 over a field of characteristic 0. We give expl icit formulae for the columns of the decomposition matrices indexed by all 2-regular partitions with 1 or 2 parts and an algorithm for calcu lating the columns of the decomposition matrix indexed by partitions w ith 3 parts. Combining these results we find all of the rows of the de composition matrices which are indexed by partitions with at most four parts. All this is accomplished by means of a more general theory whi ch begins by showing that the decomposition numbers in the columns of the decomposition matrices indexed by 2-regular partitions with ''enor mous 2-cores'' are Littlewood-Richardson coefficients. (C) 1996 Academ ic Press, Inc.