2-Variable generalized hermite matrix polynomials and lie algebra representation **

In this paper, we introduce the 2-variable generalized Hermite matrix polynomials (2VGHMaP) Hnγ(x, y; A) and discuss their special properties. Further we use the representation theory of the harmonic oscillator Lie algebra G(0,1) to derive certain results involving these polynomials. Furthermore, as applications of our main results, we derive the generating relations for the ordinary as well as matrix polynomials related to 2VGHMaP Hnγ(x, y; A).