Some results obtained by application of the LLT algorithm

Sinéad Lyle

Abstract

For every Hecke algebra of type A, we may define a decomposition matrix; the structure of each such matrix is well-known, but in general there is no way to compute the entries. An exception is the Hecke algebra over the field of complex numbers. Here a recursive algorithm, the LLT algorithm, will produce the decomposition matrices - in fact, the resulting matrix provides a 'first approximation' to the decomposition matrix of an arbitrary Hecke algebra of type A. The LLT algorithm is, however, recursive on n. We show that, in the case of some simple partitions, it is possible to use the algorithm to obtain general results; in particular, given a Specht module corresponding to a partition with at most three parts, we will find its composition factors. We also give an indication of the situation in which the partition in question has four parts.

AMS Subject Classification: Primary 20C08.