Rogers-Ramanujan type identities and nil-DAHA (Q2437547)

In this paper the theory of Fourier transform of the nilpotent double affine Hecke algebras is applied to Rogers-Ramanujan type identities. In fact, the author used the double affine Hecke algebra-Fourier transform of \(q\)-Hermite polynomials multiplied by level-one theta functions to obtain expansions of products of any number of such theta functions in terms of the \(q\)-Hermite polynomials. The relation to Rogers dilogarithm and Nahm's conjecture among other applications are also discussed.