  In 1971 Griffiths used a generating function to define polynomials in d
variables orthogonal with respect to the multinomial distribution. The
polynomials possess a duality between the discrete variables and the degree
indices. In 2004 Mizukawa and Tanaka related these polynomials to character
algebras and the Gelfand hypergeometric series. Using this approach they
clarified the duality and obtained a new proof of the orthogonality. In the
present paper, we interpret these polynomials within the context of the Lie
algebra sl_{d+1}. Our approach yields yet another proof of the orthogonality.
It also shows that the polynomials satisfy d independent recurrence relations
each involving d^2+d+1 terms. This combined with the duality establishes their
bispectrality. We illustrate our results with several explicit examples.
