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 ofHamiltonian 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 $L$: $L=bigopluslimits_{qinbbz}L_{[q],I}$, 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 $U_{chi}(L)$-moduleis induced from a simple $U_{chi}(L_{[0],I})$-module.