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Article

Rogers-Ramanujan type identities and Nil-DAHA

Advances in Mathematics. 2013. Vol. 248. No. 25. P. 1050-1088.
Cherednik I., Feigin B. L.

Using the DAHA-Fourier transform of q-Hermite polynomials multiplied by level-one theta functions, we obtain expansions of products of any number of such theta functions in terms of the q-Hermite polynomials. An ample family of modular functions satisfying Rogers-Ramanujan type identities for arbitrary (reduced, twisted) affine root systems is obtained as an application. A relation to Rogers dilogarithm and Nahm's conjecture is discussed. The q-Hermite polynomials are closely related to the Demazure level-one characters in the twisted case (Sanderson, Ion), which connects our formulas to tensor products of level-one integrable Kac-Moody modules, their coset theory and the level-rank duality. © 2013 Elsevier Inc.