Will the fundamental representation $\pi\_n$ of type $C\_n$, for $n > 3$, have weight spaces of dimension greater than $1$? Is there some online resource where weight space multiplicities can be calculated? If so this would make $C\_n$ the only non-exceptional type for which the first and last Dynkin node did not give an irrep with one-dimensional weight spaces. Is there any conceptual explanation for this?



Weight space dimension of the fundamental representation $\pi_n$ for type $C_n$
The LiE software does these calculations, and is available on line:


<http://wwwmathlabo.univ-poitiers.fr/~maavl/LiE/form.html>


