Bivariate Degenerate Hermite Polynomials in the Framework of Lie Algebra K5

Abstract

In this article, the matrix elements of the representation of the 5-dimensional Lie algebra K5 are obtained for the first time. The bivariate degenerate Hermite polynomials Hm(z1,z2|τ) are considered within the context of this representation. Further, employing the Lie algebraic techniques, certain specific results concerning these polynomials are established. Some examples providing the implicit formulas for the polynomials related to the polynomials Hm(z1,z2|τ) are considered. Integral equations for these polynomials are also explored.

Keywords: Lie group, Lie algebra K5, Generating relations, Representation theory, 2-Variable degenerate Hermite polynomials