On irreducible p,q‐representations of Lie algebras \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {G} (0,1)$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {G} (0,0)$\end{document}

In this paper, the irreducible p, q‐representations of the Lie algebras $\mathcal {G}(0,1)$ and $\mathcal {G}(0,0)$ are discussed. We prove two theorems that classify certain irreducible p, q‐representations of these Lie algebras and construct their one variable models in terms of p, q‐derivative and dilation operators. As an application, we derive a p, q‐special function identity based on one such model.