论文标题
$ e_ {7（7）} $的狄拉克系列
Dirac series of $E_{7(7)}$
论文作者
论文摘要
本文分类了$ e_ {7（7）} $的所有狄拉克系列（即具有非零狄拉克共同体的不可约统一表示）。增强1969年的Helgason-Johnson在$ e_ {7（7）} $上绑定的是一种关键成分。我们的计算部分支持Vogan的基本平行教（FPP）猜想。作为应用程序，当传递到Dirac指数时，我们继续发现Dirac共同体的偶数和奇数部分之间的取消。此外，我们第一次找到了Dirac系列，其最低$ K $ types具有多重性。
This paper classifies all the Dirac series (that is, irreducible unitary representations having non-zero Dirac cohomology) of $E_{7(7)}$. Enhancing the Helgason-Johnson bound in 1969 for the group $E_{7(7)}$ is one key ingredient. Our calculation partially supports Vogan's fundamental parallelepiped (FPP) conjecture. As applications, when passing to Dirac index, we continue to find cancellation between the even part and the odd part of Dirac cohomology. Moreover, for the first time, we find Dirac series whose spin lowest $K$-types have multiplicities.
