## 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.

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