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.

中文翻译：

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非对称 Rogers-Ramanujan 和和厚 Demazure 模块

我们考虑以 $t=\infty$ 处的非对称 Macdonald 多项式除以它们的范数来扩展与任意根系统相关的 theta 函数的乘积。后者被识别为 Demazure 切片的分级特征，厚（上）一级 Demazure 模块的一些规范商，与最近的广义（非对称）全局 Weyl 模块理论直接相关。Cherednik-Feigin 考虑的对称 Rogers-Ramanujan 型级数预计会有这种解释；非对称设置似乎是实现这一目标所必需的。作为一个应用，非对称 Rogers-Ramanujan 级数的系数提供了在 Demazure 切片方面的一级 Kac-Moody 表示的张量积的展开的多重性的公式。