Three addition theorems for someq-Krawtchouk polynomials

Theq-Krawtchouk polynomials are the spherical functions for three different Chevalley groups over a finite field. Using techniques of Dunkl to decompose the irreducible representations with respect to a maximal parabolic subgroup, we derive three addition theorems. The associated polynomials are related to affine matrix groups.During the preparation of this paper the author was partially supported by NSF grant MCS78-02410.