## 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.