论文标题
$ e_ {7（-5）} $的狄拉克系列
Dirac series of $E_{7(-5)}$
论文作者
论文摘要
使用锐化的Helgason-Johnson绑定，本文将所有不可约合的统一表示与$ e_ {7（-5）} $的非零狄拉克共同体分类。作为一个应用程序，我们发现Dirac共同体的偶数部分和奇数部分之间的取消是在某些$ e_ {7（-5）} $的单一表示情况下继续发生的。假设无限字符是不可或缺的，我们进一步改善了以$ e_ {7（-5）} $限制的Helgason-Johnson。这应该有助于人们理解该群体的统一双重双重的一部分。
Using the sharpened Helgason-Johnson bound, this paper classifies all the irreducible unitary representations with non-zero Dirac cohomology of $E_{7(-5)}$. As an application, we find that the cancellation between the even part and the odd part of the Dirac cohomology continues to happen for certain unitary representations of $E_{7(-5)}$. Assuming the infinitesimal character being integral, we further improve the Helgason-Johnson bound for $E_{7(-5)}$. This should help people to understand (part of) the unitary dual of this group.
