Dimensions of representations obtained by branching rule are incorrect
Consider $\mathrm{SO}_3\subset\mathrm{GL}_3$ as fixed points of the obvious involution. Then we should be able to compute restrictions of representations via the "symmetric" branching rule:
GL3 = WeylCharacterRing(['A', 2])
B1=WeylCharacterRing(['B',1])
V=GL3(3,2,-1); V.degree()
Sage says the output it 24. Now if we restrict to $\mathrm{SO}_3$, we get
b = branching_rule("A2","B1")
V.branch(B1, rule=b)
Sage says the output is
B1(1) + B1(2) + B1(3) + B1(4)
and the result of
[B1(1).degree(), B1(2).degree(), B1(3).degree(), B1(4).degree()]
is
[1, 2, 3, 4]
which is clearly wrong if $\mathrm{dim}V=24$. As noted in another question ten years ago (I have too little karma to post links), Sage seems to not be able to do this properly.
Is this a problem with Sage, or am I doing something wrong?