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).