论文标题
关于跨度的Barbasch-Vogan二元性的概念
On the notion of metaplectic Barbasch-Vogan duality
论文作者
论文摘要
与实际还原线性群的Barbasch-Vogan二元性类似，我们引入了对真实元位基团的表示理论有用的二元性概念。这是一个复杂的符号谎言代数中的nilpotent轨道集的地图，其范围由所谓的元容器特殊的nilpotent轨道组成。我们将这种二元性概念与原始理想理论联系起来，并将特殊单位表示的概念扩展到真实的元素群体。我们还根据Weyl组表示的双重细胞来解释二元图。
In analogy with the Barbasch-Vogan duality for real reductive linear groups, we introduce a duality notion useful for the representation theory of the real metaplectic groups. This is a map on the set of nilpotent orbits in a complex symplectic Lie algebra, whose range consists of the so-called metaplectic special nilpotent orbits. We relate this duality notion with the theory of primitive ideals and extend the notion of special unipotent representations to the real metaplectic groups. We also interpret the duality map in terms of double cells of Weyl group representations.
