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arXiv · 1802.03819

Nonsymmetric Rogers-Ramanujan sums and thick Demazure modules

Ivan Cherednik·Syu Kato
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Abstract

We consider expansions of products of theta-functions associated with arbitrary root systems in terms of nonsymmetric Macdonald polynomials at $t=\infty$ 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.

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BibTeXRIS

Ivan Cherednik, Syu Kato. 2018-02-11. Nonsymmetric Rogers-Ramanujan sums and thick Demazure modules. https://arxiv.org/abs/1802.03819

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