Associated Lie Algebras of one-variable and Bivariate Hermite polynomials and New Generating Functions

This paper presents the symmetries of differential equations associated with one-variable and Bivariate Hermite polynomials by proposing a representation of Lie algebra sl 2,R for these differential operators. Applying the Baker-Campbell-Hausdorff formula to these algebras, results in new relations and generating functions in one-variable and Bivariate Hermite polynomials. A general form of sl 2,R representation for other orthogonal polynomials such as Laguerre polynomials is introduced.