Polynomial identities, indices, and duality for the N=1 superconformal model SM(2,4v)

We prove polynomial identities for the N = 1 superconformal model SM(2, 4v) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations for q-series on the Fermionic side. We use these polynomials to demonstrate a dual relation under q-->q(-1) between SM(2, 4v) and M(2v - 1, 4v). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.