We introduce a class of modules over Kac–Moody superalgebras; we call these modules snowflake modules. These modules are characterized by invariance property of their characters with respect to a certain subgroup of the Weyl group. Examples of snowflake modules appear as admissible modules in representation theory of affine vertex algebras and in the classification of bounded weight modules. Using these modules we prove Arakawa’s theorem for the Lie superalgebra $\mathfrak{𝔬}\mathfrak{𝔰}\mathfrak{𝔭}{(1|2\ell )}^{(1)}$.

中文翻译：

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Kac–Moody 超代数的雪花模和 Enright 函子

我们在 Kac-Moody 超代数上引入了一类模块；我们称这些模块为雪花模块。这些模块的特征在于它们的特征相对于 Weyl 群的某个子群的不变性。雪花模的例子在仿射顶点代数的表示论和有界权重模的分类中作为可容许模出现。使用这些模块，我们证明了李超代数的荒川定理$\mathfrak{𝔬}\mathfrak{𝔰}\mathfrak{𝔭}{(1|2\ell )}^{(1)}$.