On Wed, Jun 02, 2010 at 02:27:16PM -0700, Anne Schilling wrote:
> >Yes! In this test, we want to check not only translations by roots
> >(preserving polygons) but also translations by weights (preserving
> >alcoves only); e.g. play with the extended Weyl group. And there is
> >the same question of appropriate "translation factors" for the
> >fundamental weights. It seems that using the `c_i` just does the
> >job. I remember having a rationale for this for untwisted/dual
> >thereof; for type BC, this seems to just work (whereas using the same
> >translation factors as for the roots breaks); but that might be plain
> >luck, and the current tests only ensure that the factors are not too
> >small; they might be too large.
>
> Ok, then this is correct since the lattice of the extended Weyl group is
> indeed
>
> \oplus_{i \in I \setminus {0} } \ZZ c_i \omega_i
>
> even for A_{2n}^{(2)}.
Perfect. Then maybe the desired conceptual definition for the `c_i`
should be as the "translation factors" for the fundamental weights?
At some point we should add a couple more refs in the code, in
particular about such technical topics.
Thanks for checking!
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
--
You received this message because you are subscribed to the Google Groups
"sage-combinat-devel" group.
To post to this group, send email to sage-combinat-de...@googlegroups.com.
To unsubscribe from this group, send email to
sage-combinat-devel+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/sage-combinat-devel?hl=en.
