Lie-theoretic generating relations of Hermite 2D polynomials

In this paper, we derive some generating relations involving Hermite 2D polynomials (H2DP) Hm,n(U;x,y), of two variables with an arbitrary 2D matrix U as parameter using Lie-theoretic approach. Certain (known or new) generating relations for the polynomials related to H2DP are also obtained as special cases.