Invariant Differential Operators on Certain Nilpotent Homogeneous Spaces
Invariant Differential Operators on Certain Nilpotent Homogeneous Spaces
复制标题
某些幂零齐次空间上的不变微分算子
DOI：
10.1007/s006050170009
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
J. Ludwig
中科院分区：
文献类型：
--
作者：
A. Baklouti;J. Ludwig
设G是幂零连通李群和单连通李群，G是G的解析子群。设，是H的一个酉特征标，令。假设τ的所有不可约分量的重数都是有限的。Corwin和Greenleaf证明了τ的Schwartz-空间上与τ可交换的微分算子代数同构于仿射空间上的H-不变多项式代数。本文证明了这个猜想的条件下，存在一个子代数的所有通用元素极化。我们还证明了如果是的理想，则τ的有限重数等价于代数是交换的。
Abstract. Let be a nilpotent connected and simply connected Lie group, and an analytic subgroup of G. Let , be a unitary character of H and let . Suppose that the multiplicities of all the irreducible components of τ are finite. Corwin and Greenleaf conjectured that the algebra of the differential operators on the Schwartz-space of τ which commute with τ is isomorphic to the algebra of H-invariant polynomials on the affine space . We prove in this paper this conjecture under the condition that there exists a subalgebra which polarizes all generic elements in . We prove also that if is an ideal of , then the finite multiplicities of τ is equivalent to the fact that the algebra is commutative.