LieArt --- 3 different 8 dimensional irreducible representation of $mathrm{SO}(8)$ and their decompositions

Question

I am using the LieArt which you can download freely online https://arxiv.org/pdf/1206.6379.pdf

There are three different 8 dimensional $mathrm{SO}(8)$  irreducible representations, formally it is written as 8$_v$,  8$_s$, 8$_c$. See p.26 of https://arxiv.org/pdf/1206.6379.pdf

Question: What will we call out of these three different 8 dimensional $mathrm{SO}(8)$  irreducible representations through Mathematica? Are they represented by these?

Irrep[SO8][IrrepPrime[8, 0]]

Irrep[SO8][IrrepPrime[8, 1]]

Irrep[SO8][IrrepPrime[8, 2]]

but they seem not work?

arow257 · Answer

You should be able to create 8-dimensional irreps of SO(8) in LieART by using Dynkin labels
Irrep[D][1,0,0,0]
Irrep[D][0,0,1,0]
Irrep[D][0,0,0,1]

where the (1000) Dynkin label corresponds to the $mathbf{8}_text{v}$, the (0010) Dynkin label corresponds to the $mathbf{8}_text{c}$ irrep, and the (0001) Dynkin label corresponds to the $mathbf{8}_text{s}$ irrep. Similarly, you should be able to specify any other irrep of SO(8) in the same way as long as you know the Dynkin label, which is given in the first column of the table you posted.
As far as I know, the authors did not include any alternative ways of entering SO(8) irreps especially, but they did recently release a new version, so perhaps there are new modifications that I don't know about yet.

LieArt --- 3 different 8 dimensional irreducible representation of $mathrm{SO}(8)$ and their decompositions

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