论文标题
超对称空间上的幽灵发行
Ghost distributions on supersymmetric spaces II: basic classical superalgebras
论文作者
论文摘要
我们研究了基本古典谎言超级级别的超对称空间上的幽灵分布。我们介绍了隔行对的概念，这是$（\ mathfrak {g}，\ mathfrak {k}）$和$（\ mathfrak {g}，\ mathfrak {k}'）$ aff iwasawa decompositions的概念。对于这样的对，我们定义一个幽灵代数，概括了$ \ Mathcal {u} \ Mathfrak {g} $由gorelik定义的。我们将这个代数视为超对称空间本身的$ g $ equivariant运算符的代数，对于某些成对，“特殊”的代数是“特殊”的代数，我们将运营商视为$ g/k $上的扭曲等级差异操作员。我们还表明，Harish-Chandra形态具有含义，计算其所有排名一对的图像，并在$（\ Mathfrak {g}，\ Mathfrak {K k}）$时为图像提供猜想。
We study ghost distributions on supersymmetric spaces for the case of basic classical Lie superalgebras. We introduce the notion of interlaced pairs, which are those for which both $(\mathfrak{g},\mathfrak{k})$ and $(\mathfrak{g},\mathfrak{k}')$ admit Iwasawa decompositions. For such pairs we define a ghost algebra, generalizing the subalgebra of $\mathcal{U}\mathfrak{g}$ defined by Gorelik. We realize this algebra as an algebra of $G$-equivariant operators on the supersymmetric space itself, and for certain pairs, the `special' ones, we realize our operators as twisted-equivariant differential operators on $G/K$. We additionally show that the Harish-Chandra morphism is injective, compute its image for all rank one pairs, and provide a conjecture for the image when $(\mathfrak{g},\mathfrak{k})$ is interlaced.
