论文标题
$ gl（n，\ mathbb {r}）$的狄拉克系列$
Dirac series of $GL(n, \mathbb{R})$
论文作者
论文摘要
$ gl（n，\ mathbb {r}）$的统一双重偶数在1980年代被Vogan分类。专注于$ gl（N，\ Mathbb {r}）$具有半综合无限字符的不可约合的统一表示，我们发现SPEH表示和特殊的单位表示形式是基础。通过查看它们的$ k $类型以及使用Blattner-type公式，我们获得了所有不可约合的单一$（\ Mathfrak {g}，k）$ - 具有$ gl（n，\ mathbb {r}）$的$ gl（n，\ mathb {r}）$的dirac gromology的模块，以及k的$ k $ k $ k的$ k.此外，类似于[dw1]中给出的$ gl（n，\ mathbb {c}）$ case，我们计算$ gl（n，\ mathbb {r}）$的fs scatered表示的数量。
The unitary dual of $GL(n, \mathbb{R})$ was classified by Vogan in the 1980s. Focusing on the irreducible unitary representations of $GL(n, \mathbb{R})$ with half-integral infinitesimal characters, we find that Speh representations and the special unipotent representations are building blocks. By looking at the $K$-types of them, and by using a Blattner-type formula, we obtain all the irreducible unitary $(\mathfrak{g}, K)$-modules with non-zero Dirac cohomology of $GL(n, \mathbb{R})$, as well as a formula for (one of) their spin-lowest $K$-types. Moreover, analogous to the $GL(n,\mathbb{C})$ case given in [DW1], we count the number of the FS-scattered representations of $GL(n, \mathbb{R})$.
