Nonsymmetric Rogers-Ramanujan sums and thick Demazure modules
Abstract
We consider expansions of products of theta-functions associated with arbitrary root systems in terms of nonsymmetric Macdonald polynomials at divided by their norms. The latter are identified with the graded characters of Demazure slices, some canonical quotients of thick (upper) level-one Demazure modules, directly related to recent theory of generalized (nonsymmetric) global Weyl modules. The symmetric Rogers-Ramanujan-type series considered by Cherednik-Feigin were expected to have some interpretation of this kind; the nonsymmetric setting appeared necessary to achieve this. As an application, the coefficients of the nonsymmetric Rogers-Ramanujan series provide formulas for the multiplicities of the expansions of tensor products of level-one Kac-Moody representations in terms of Demazure slices.
Cite
@article{arxiv.1802.03819,
title = {Nonsymmetric Rogers-Ramanujan sums and thick Demazure modules},
author = {Ivan Cherednik and Syu Kato},
journal= {arXiv preprint arXiv:1802.03819},
year = {2018}
}