[GAP Forum] Modules over general and not so general algebras

[Jean MICHEL]

On Fri, Feb 01, 2013 at 03:38:08PM +0100, Johannes Hahn wrote:
> Is there an elegant way to implement (finite-dimensional) modules over my 
> favorite algebra? My algebra is finite dimensional and I would GAP tell 
> this if it needs to know, but I don't want to spell out an explicit basis 
> and structure constants for the algebra. (More to the point: I work with 
> Hecke algebras and they get way to big for this, if the Coxeter group is 
> big, say E_7, E_8)
>
> I do not actually need the algebra, I just want to do some computations 
> with the matrices of the representation. There seems no way to define an 
> algebra by generators and relations because GAP seemingly wants to do some 
> calculations and of course this goes wrong in the general case and even in 
> my special case GAP doesn't know that there are normalforms for the 
> elements of my algebra etc. (And I cannot find a way to tell GAP this)

Matrices  for  all  irreducible  representations  of  the Hecke algebras of
finite  Coxeter group are implemented in  the GAP3 package CHEVIE. There is
also an implementation of various bases of these algebras.

See www.math.jussieu.fr/~jmichel/chevie
------------------------------------------------------------------------------
Jean MICHEL, Groupes et representations, IMJ-PRG UMR7586 tel.(33)157279144
Bureau 639 Bat. Sophie Germain Case 7012 - 75205 PARIS Cedex 13