限制Hamiltonian型及Contact型李代数的不可约表示

设L=H（2r;1）或K（2r+1;1）是定义在特征p>2的代数封闭域F上的限制Hamiltonian型或Contact型李代数.在对广义Jacobson-Witt代数及特殊代数不可约表示的研究基础上,通过定义L的如下阶化:L=L_q],I,其中I是{1,2,…,r}的子集,得到当p-特征函数χ是正则半单时,所有不可约U_χ（L）-模都是从不可约U_χ(L_O].I)-模诱导的.

Irreducible Representations of Restricted Lie Algebras of Hamiltonian Type and Contact Type

Let $L=H(2r;\textbf{1})$ or $K(2r+1;\textbf{1})$ be a restricted Lie algebra of Hamiltonian type or contact type over an algebraically closed field $F$ of characteristic $p>2$. Based on the study of irreducible representations of generalized Jacobson-Witt algebras and special algebras, with the aid of the gradation structure of $L$: $L=\bigoplus\limits_{q\in\bbz}L_{q],I}$, where $I$ is a subset of $\{1,2,\cdots,r\}$, it is proved that when the $p$-characteristic function $\chi$ is regular semisimple, each simple $U_{\chi}(L)$-module is induced from a simple $U_{\chi}(L_{0],I})$-module.