Hecke algebras of type A with q=-1

Gordon James and Andrew Mathas

Keywords

Hecke algebras, symmetric groups, decomposition numbers, Littlewood-Richardson Rule.

Status

J. Algebra, 184, (1996), 102-158.
MR97h:20017.

Abstract

In this paper we study the decomposition matrices of the Hecke algebras of type~A with q=-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.

Andrew Mathas
15th May 1996.