The notion of a factorized \(A_2\) -Leonard pair is introduced. It is defined as a rank 2 Leonard pair, with actions in certain bases corresponding to the root system of the Weyl group \(A_2\) , and with some additional properties. The functions arising as entries of transition matrices are bivariate orthogonal polynomials (of Tratnik type) with bispectral properties. Examples of factorized \(A_2\) -Leonard pairs are constructed using classical Leonard pairs associated to families of orthogonal polynomials of the (q-)Askey scheme. The most general examples are associated to an intricate product of univariate (q-)Hahn and dual (q-)Hahn polynomials.
