Lie theory of polynomials of the form \(F_ D\) via Mellin transformation (Q1189884)

This paper constructs models of irreducible representations of complex Lie algebras: \(\text{sl}(2,\mathbb{C})\) for the complex special linear algebra, \(G(0,1)\) for the oscillator algebra, with Laguerre polynomials acting as basis vectors. The obtained models are expressed in terms of difference-differential operators through Mellin transformation.