Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras

We classify finite-dimensional tame modules over the orthosymplectic Lie superalgebras. For these modules we show that their characters are given by the Kac-Wakimoto character formula, thus establishing the Kac Wakimoto conjecture for the orthii-symplectic Lie superalgebras. We further relate the Kac-Wakimoto formula to the super Jacobi polynomials of Sergeev and Veselov, and shoW that these polynomials, up to a sign, give the super characters for these tame modules. (C) 2016 Elsevier Inc. All rights reserved.