Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4ν)

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We prove polynomial identities for the N=1 superconformal model SM(2,4ν) 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(2,4ν) and M(2ν-1,4ν). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.