Enveloping superalgebra U(osp (1 vertical bar 2)) and orthogonal polynomials in discrete indeterminate

Let A be an associative simple (central) superalgebra over C and L an invar iant linear functional on it (trace). Let a bar right arrow a(t) be an anti automorphism of A such that (a(t))(t) = (-1)(p(a))a, where p(a) is the pari ty of a, and let L(a(t)) = L (a). Then A admits a nondegenerate supersymmet ric invariant bilinear form <a,b > = L(ab(t)). For A = U(sl( 2))/m, where m is any maximal ideal of U(sl( 2)), Leites and I have constructed orthogona l basis in A whose elements turned out to be, essentially, Chebyshev ( Hahn ) polynomials in one discrete variable. Here I take A = U(osp(1|2))/m for a ny maximal ideal m and apply a similar procedure. As a result we obtain eit her Hahn polynomials over C[tau], where tau (2) epsilon C, or a particular case of Meixner polynomials, or - when A = Mat( n+1|n)- dual Hahn polynomia ls of even degree, or their ( hopefully, new) analogs of odd degree. Observ e that the nondegenerate bilinear forms we consider for orthogonality are, as a rule, not sign definite.