In this paper, we construct the Heisenberg-Virasoro algebra in the framework of the $\mathcal{ R}(p,q)$-deformed quantum algebras. Moreover, the $\mathcal{ R}(p,q)$-Heisenberg-Witt $n$-algebras is also investigated. Furthermore, we generalize the notion of the elliptic hermitian matrix models. We use the constraints to evaluate the $\mathcal{ R}(p,q)$-differential operators of the Virasoro algebra and generalize it to higher order differential operators. Particular cases corresponding to quantum algebras existing in literature are deduced.
Categories: math.QA math-ph math.MP