Ghazala Yasmin (Aligarh Muslim University, Aligarh, India)

Hermite Matrix based Polynomials of two Variables and Lie Algebraic Techniques

Abstract:
   In this paper, we introduce the 2-variable generalized Hermite matrix polynomials _HH_n^λ(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 matrix polynomials related to _HH_n^λ(x,y;A).