Hecke Algebras of TypeAwithq=−1 Original Research Article

In this paper we study the decomposition matrices of the Hecke algebras of typeAwithq=−1 over a field of characteristic 0. We give explicit formulae for the columns of the decomposition matrices indexed by all 2-regular partitions with 1 or 2 parts and an algorithm for calculating the columns of the decomposition matrix indexed by partitions with 3 parts. Combining these results we find all of the rows of the decomposition matrices which are indexed by partitions with at most four parts. All this is accomplished by means of a more general theory which begins by showing that the decomposition numbers in the columns of the decomposition matrices indexed by 2-regular partitions with “enormous 2-cores” are Littlewood–Richardson coefficients.