论文标题
Gelfand-kirillov尺寸和标量类型的常规Verma模块的经典谎言代数
Gelfand-Kirillov dimensions and Reducibility of scalar type generalized Verma modules for classical Lie algebras
论文作者
论文摘要
令$ \ mathfrak {g} $为级别的lie代数，$ \ mathfrak {p} $是最大的抛物线副词。令$ m $为$ \ mathfrak {p} $的一维表示诱导的广义Verma模块。这样的$ M $称为标量类型的广义Verma模块。它的简单商$ l $是最高的重量。在本文中，我们将通过计算$ L $的Gelfand-Kirillov尺寸来确定这种标量类型的广义Verma模块的降低性。
Let $\mathfrak{g}$ be a classial Lie algebra and $\mathfrak{p}$ be a maximal parabolic subalgebra. Let $M$ be a generalized Verma module induced from a one dimensional representation of $\mathfrak{p}$. Such $M$ is called a scalar type generalized Verma module. Its simple quotient $L$ is a highest weight moudle. In this paper, we will determine the reducibility of such scalar type generalized Verma modules by computing the Gelfand-Kirillov dimension of $L$.
