Rogers-Ramanujan type identities and Nil-DAHA
Abstract
In the theory of the Nil-DAHA Fourier transform, the inner products of q-Hermite polynomials for the measure function multiplied by a level one theta function are the key. They are used to 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. Some of our q-series can be identified with known ones, but their interpretation seems new. Using that the q-Hermite polynomials are closely related to the Demazure level one characters in the twisted case (Sanderson, Ion), we outline a connection of our formulas to the level one integrable Kac-Moody modules and the coset theory. Several instances of the level-rank duality are provided.
Cite
@article{arxiv.1209.1978,
title = {Rogers-Ramanujan type identities and Nil-DAHA},
author = {Ivan Cherednik and Boris Feigin},
journal= {arXiv preprint arXiv:1209.1978},
year = {2012}
}
Comments
v2: extending the dilogarithm part, adding level two formulas (thanks to Ole Warnaar); v3: more on dilogarithms (thanks to Tomoki Nakanishi), adding references and some instances of level-rank duality; v4: editing