Rogers–Ramanujan type identities and Nil-DAHA

By I. Cherednik, Boris Feigin. 2012

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Abstract 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 Nahmʼs 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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bb6e747d2fa8f185c2ac5dbaffa538016265f249

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Citations in the corpus

A framework of Rogers–Ramanujan identities and their arithmetic properties (2014, background): “linked to algebraic geometry [23, 37], K-theory [28], conformal field theory [10, 44, 52], group theory [32], Kac–Moody, Virasoro, vertex and double affine Hecke algebras [25, 31, 50, 51, 53, 54, 55, 56], knot theory [6, 39, 40], modular forms [16, 17, 18, 19, 20, 21, 22, 63], orthogonal polynomials”