Highest weight modules associated with classical irreducible regular prehomogeneous vector spaces of commutative parabolic type
Highest weight modules associated with classical irreducible regular prehomogeneous vector spaces of commutative parabolic type
复制标题
与交换抛物型类型的经典不可约正则预齐次向量空间相关的最高权重模块
DOI：
10.11501/2964161
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发表时间：
1991
影响因子：
0.4
通讯作者：
S. Suga
中科院分区：
文献类型：
--
作者：
S. Suga
设G是具有李代数g的连通复李群，G(0)是G的李子代数g(0)对应的连通子群，我们进一步假定G(0)，g(ZTL)是不可约正则准齐次向量空间[6]，[8]。设DX是抛物子代数P=g(O)-(-g(L))的一维表示，CDλ是它的表示空间。设C/(G)和U(P)分别是g和t>；的泛包络代数。我们用V(Dx)表示由d\诱导的广义Verma模：
Let G be a connected complex Lie group with Lie algebra g, and G(0) the connected subgroup of G corresponding to the Lie subalgebra g(0) of g. We further assume that the pairs (G(0), g(ztl)) are irreducible regular prehomogeneous vector spaces [6], [8]. Let dx be a 1-dimensional representation of the parabolic subalegebra P=g(O)-(-g(l), and Cdλ its representation space. Let C/(g) and U(p) be the universal enveloping algebras of g and t>, respectively. We denote by V(dX) the generalized Verma module induced from d\: