I'm trying to find out what all the generators of the SU(5) group explicitly look like but I can't find them anywhere.(adsbygoogle = window.adsbygoogle || []).push({});

I know what the first 12 look like:

[tex]

T^{1,2,3} = \begin{pmatrix} 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & \sigma^{1,2,3} & \\ 0 & 0 & 0 & & \end{pmatrix},

T^{4} = \begin{pmatrix} \frac{-1}{3} & 0 & 0 & 0 & 0 \\ 0 & \frac{-1}{3} & 0 & 0 & 0 \\ 0 & 0 & \frac{-1}{3} & 0 & 0\\ 0 & 0 & 0 & \frac{1}{2} & 0 \\ 0 & 0 & 0 & 0 & \frac{1}{2} \end{pmatrix},

T^{\alpha = 5,...,12} = \begin{pmatrix} \lambda^{\alpha - 4} & & & 0 & 0 \\ & & & 0 & 0 \\ & & & 0 & 0\\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}

[/tex]

where [itex]\sigma^{1,2,3}[/itex] are the Pauli matrices of SU(2) and [itex]\lambda^{1,2,3,4,5,6,7,8}[/itex] are the Gell-Mann matrices of SU(3). However, there are another 12 that I can't seem to find anywhere:

[tex]

T^{\alpha=13,...,24} = \begin{pmatrix} 0 & 0 & 0 &m ^{13+n} & \\

0 & 0 & 0 & & \\

0 & 0 & 0 & & \\

(m^{13+n})^{\dagger} & & & 0 & 0 \\

& & & 0 & 0 \end{pmatrix} (n = 0, 1, ..., 11)

[/tex]

where [itex]m^{13 + n}[/itex] are [itex]3\times2[/itex] matrices. Can anyone show me?

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# What are all the generators of SU(5)?

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