Lie-theoretic generating relations of two variable Laguerre polynomials

Abstract

Generating relations involving two variable Laguerre polynomials $L_{n}(x,y)$ are derived. The process involves the construction of a three dimensional Lie algebra isomorphic to special linear algebra $sl(2)$ with the help of Weisner's method by giving suitable interpretations to the index $n$ of the polynomials $L_{n} (x,y)$