These indeed are the marks or labels in Kac' tables Aff1 and Aff2. We can
do the following:
sage: ct = CartanType(['E',6,2])sage:
L=RootSystem(ct).weight_lattice(extended=True)
sage: a = ct.a(); sum(a[i]*L.simple_root(i) for i in L.index_set())
delta
This produces delta for every Cartan Type except ['A', 2n, 2] aka ['BC', n,
2]. In
that case, it produces 2*delta.
On Tuesday, February 18, 2014 11:19:15 PM UTC-8, Nicolas M. Thiery wrote:
>
> On Tue, Feb 18, 2014 at 08:44:57PM -0800, Anne Schilling wrote:
> > Regarding the labels you are looking for, perhaps they are these (I do
> not have Kac's book
> > with me right not):
> >
> > sage: R = RootSystem(['A',2,1])
> > sage: C = R.cartan_type()
> > sage: C
> > ['A', 2, 1]
> > sage: C.a()
> > Finite family {0: 1, 1: 1, 2: 1}
> > sage: C.acheck()
> > Finite family {0: 1, 1: 1, 2: 1}
>
> which are shorthand aliases for the more explicit methods
> col_annihilator and row_annihilator respectively.
>
>
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