Specht is a package for computing decomposition matrices; this section describes the functions available for accessing these matrices directly. In addition to decomposition matrices, Specht also calculates the ``crystallized decomposition matrices'' of [LLT], and the ``adjustment matrices'' introduced by James [J] (and Geck [G]).
Throughout Specht we place an emphasis on calculating the projective
indecomposable modules, and hence upon the columns of decomposition
matrices. This approach seems more efficient than the traditional
approach of calculating decomposition matrices by rows; ideally both
approaches should be combined (as is done by
In principle, all decomposition matrices for all Hecke algebras defined over a field of characteristic zero are available from within Specht. In addition, the decomposition matrices for all q--Schur algebras with n le 10 and all values of e and the p--modular decomposition matrices of the symmetric groups Sym_n for n<15 are in the Specht library files.
If you are using Specht regularly to do calculations involving certain values of e it would be advantageous to have Specht calculate and save the first 20 odd decomposition matrices that you are interested in. So, for <e>=4 use the commands:
gap> H:=Specht(4);; for n in [8..20] do > SaveDecompositionMatrix(DecompositionMatrix(H,n)); > od;
Alternatively, you could save the crystallized decomposition matrices. Note that for <n><2<e> the decomposition matrices are known (by Specht) and easy to compute.
Previous Up Top Next