Severin Pošta
Realizations of $\mathrm{sl}(3)$
Although not honoured as one of the “fundamental group of physics”, despite the Lie group $\mathrm{SL}(3,\mathbb{C})$/$\mathrm{SL}(3,\mathbb{R})$ and the associated Lie algebra play an important role in the symmetries of ordinary differential equations. It is therefore worthwhile to have realizations of this algebra in reserve in the case they are needed. In this contribution, we will be interested in how the realizations of $\mathrm{sl}(3)$ calculated by Shirokov's method look like when using the classification of $\mathrm{sl}(3)$-subalgebras up to inner automorphism, which is known thanks to Douglas and Repka.
