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2015-06-06 05:45:46 -0600 answered a question Dimensions of modules in branching
def branching_dimensions(chi):
    monomials = chi.monomials()
    coef = chi.coefficients()
    res = ""
    for i in range(len(coef)):
        res += str(coef[i]) + "*" + str(monomials[i].degree()) + " + "
    return res[:-3]
2015-06-03 09:55:46 -0600 asked a question Dimensions of modules in branching

For example, consider the following branching:

G2=WeylCharacterRing("G2",style="coroots")
adj=G2(0,1)
A1 = WeylCharacterRing("A1", style="coroots")
adj.branch(A1,rule="levi")

How can I find the dimensions of all representations that occur? In this example, we obtain:

3*A1(0) + A1(2) + 2*A1(3)

and I would like to get:

3*1 + 3 + 2*4

(Note: If I try A1(1).degree() I obtain 1 which is wrong.)

2013-04-01 09:13:29 -0600 received badge  Editor (source)
2013-04-01 08:02:03 -0600 commented question epsilon basis for roots (was graph edge labels)

No the labels are in $\alpha$-notation in SAGE. The matter is a bit more complicated since the $\epsilon$-notation has to be computed from the $\alpha$-notation. It;s just a different notation really. The problem is, that there's no $\epsilon$-notation in SAGE, since the ambient space for RootSystem is implemented via tuples of numbers.

2013-04-01 04:43:19 -0600 asked a question epsilon basis for roots (was graph edge labels)

I need an illustration of some (sub)poset of positive roots. I have a working code that produces correct labels, but they are written as sums of simple roots. I.e. the resulting graph (when exported to LaTeX) has labels such as $\alpha_1 + \alpha_2$. I would like to have these labels in $\epsilon$-notation. I.e. the previous example would read $\epsilon_1 - \epsilon_3$.

RootSystem has an ambient_space method that provides an access epsilon basis, but

  1. I am not clear on converting between these two bases

and

  1. output to LaTeX should really use $\epsilon_1 - \epsilon_3$ rather than $(1,0,-1)$.