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We prove polynomial identities for the N=1 superconformal model SM(2,4\nu)which generalize and extend the known Fermi/Bose character identities. Ourproof uses the q-trinomial coefficients of Andrews and Baxter on the bosonicside and a recently introduced very general method of producing recursionrelations for q-series on the fermionic side. We use these polynomials todemonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4\nu) andM(2\nu-1,4\nu). We also introduce a generalization of the Witten index which isexpressible in terms of the Rogers false theta functions.Comment: 41 pages, harvmac, no figures; new identities, proofs and comments  added; misprints eliminate

Polynomial identities, indices, and duality for theN=1 superconformal modelSM(2, 4v)