Hi Andrew,
> Then there are other annoyances in that the seminormal representations for
> the algebras with different quadratic relations, for example
> $(T_r-q)(T_r+1)=0$, $(T_r-q)(T_r+q^{-1})=0$ or
> $(T_r-q)(T_r+v)=0$, are all different and, of course, there are several
> different flavours of seminormal representations. Any suggestions on what we
> should try and support here would be appreciated.
Wouldn't it make most sense to use the quadratic relation
$(T_r-q)(T_r-v)=0$
since the other ones can be obtained by appropriate specialization?
> In thinking about this it seems to me that currently there is no framework in
> sage for dealing with module that has more than one "natural" basis. Is this
> right? Of course, it is possible to define
> several different CombinatoriaFreeModules and coercions between them.
Examples of how to handle this might be in
combinat/ncsf_qsym
> A final question: where should this code go? Currently the Iwahori-Hecke
> algebras are defined in sage.algebras and the seminormal matrix
> representations in sage.combinat. I think the best place might
> be to put all of this code in a new directory
> sage.algebras.iwahoriheckeagebras/
I think sage.algebras.iwahori_hecke_algebras might be best. But then
iwahori_hecke_algebra.py
should probably also be moved.
Best,
Anne
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