Whittaker modules and quasi-Whittaker modules for the Euclidean Lie algebra

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• 作者：Yan-an Cai^a ; ^{yatsai@mail.ustc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Ran Shen^b ; ^{rshen@dhu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Jiangang Zhang^c ; ^{jgzhang@shnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：17B10 ; 17B65 ; 17B68
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：220
• 期：4
• 页码：1419-1433
• 全文大小：350 K

文摘

In this paper, we classify simple Whittaker modules and simple quasi-Whittaker modules for the Euclidean Lie algebra E=e(3)$\mathcal{E}=\mathfrak{e}(3)$. We show that a simple e(3)$\mathfrak{e}(3)$-module is a Whittaker module if and only if it is a locally finite E⁺${\mathcal{E}}^{+}$-module, and it is a quasi-Whittaker module if and only if it is a locally finite P$\mathcal{P}$-module. In particular, we get a class of simple weight e(3)$\mathfrak{e}(3)$-modules which have infinite-dimensional weight spaces.