N=2 Neveu-Schwarz代数的简单限制模
Simple Restricted modules for $N=2$ Neveu-Schwarz algebra
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中文总结 AI 辅助
本文针对N=2 Neveu-Schwarz代数，构造含最高权模与Whittaker模的简单限制模，刻画其等价条件并证明特定正根元素局部有限作用时该模必为限制模。
中文摘要 AI 辅助
本文首先为N=2 Neveu-Schwarz代数𝒞构造了大量简单限制模，这些模包含最高权模和Whittaker模；接着在特定条件下精确刻画𝒞上的简单限制模，建立简单𝒞-模为限制模的若干等价条件；最后证明，若𝒞的某个特定正根元素在简单𝒞-模V上局部有限作用，则V必为限制模。
英文摘要
In this paper, we first construct many simple restricted modules for the $N=2$ Neveu-Schwarz algebra $\mathcal{L}$. These modules contain the highest weight modules and Whittaker modules. Then we precisely characterize the simple restricted modules over $\mathcal{L}$ under certain conditions, and establish several equivalent conditions for a simple \(\mathcal{L}\)-module to be restricted. Finally, we prove that if one specific positive root element of $\mathcal{L}$ acts locally finitely on a simple $\mathcal{L}$-module $V$, then $V$ must be restricted.
