Dimensions of modules in branching

asked 2015-06-03 16:55:46 +0200

vit.tucek
1 ●1 ●1 ●2

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.)

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answered 2015-06-06 12:45:46 +0200

vit.tucek
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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]

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Asked: 2015-06-03 16:55:46 +0200

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Last updated: Jun 06 '15

Dimensions of modules in branching edit

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