In this paper we follow the approach of Miller ([4]) and obtain generating relations of modified Laguerre polynomials by extending the realizations of $uparrow_{omega , mu }$ and $downarrow_{omega , mu }$ to multiplier representations of a Lie group $G(0,1)$. Many results of Miller, McBride and Srivastava and Manocha follow as special cases of our results. Generating relations of modified Laguerre
polynomials are of interest due to its connections and reductions to a number of other special functions which are well known.

Keywords: Lie group, Lie algebra, Laguerre polynomials, generating relations.