= SU6 tensor branchings to SU5
{c}
{title2=$\mathbf6\downarrow=\mathbf5\oplus\mathbf1$}
For the embedding $U\mapsto\operatorname{diag}(1,U)$, the defining <SU(6)> <representation> restricts to the defining <SU(5)> <representation> plus a <trivial representation>. Taking <dual representations>, <symmetric squares>, <exterior squares> and traceless <endomorphisms> gives $\overline{\mathbf6}\downarrow=\overline{\mathbf5}\oplus\mathbf1$, $\mathbf{21}\downarrow=\mathbf{15}\oplus\mathbf5\oplus\mathbf1$, $\mathbf{15}\downarrow=\mathbf{10}\oplus\mathbf5$, and $\mathbf{35}\downarrow=\mathbf{24}\oplus\mathbf5\oplus\overline{\mathbf5}\oplus\mathbf1$. The fixed diagonal direction in the <Adjoint representation> is $\operatorname{diag}(-5,1,1,1,1,1)$. Dimensions label <representations> of different <groups> on the two sides: the fifteen-dimensional <SU(6)> <representation> is alternating, while the fifteen-dimensional <SU(5)> <representation> is symmetric.
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