论文标题
$ \ mathrm {gl}（n）$的狄拉克系列$
Dirac series of $\mathrm{GL}(n)$ over an Archimedean field
论文作者
论文摘要
Motivated by the $(\mathfrak{g},K)$-cohomology and Dirac cohomology, we determine Dirac series of $\mathrm{GL}(n,\mathbb{H})$, and show that the spin lowest $K$-type of any Dirac series, which determines the Dirac cohomology, is unique and multiplicity-free for both $ \ mathrm {gl}（n，\ mathbb {h}）$和$ \ mathrm {gl}（n，\ mathbb {r}）$。这验证了关于$ \ mathrm {gl}（n，\ mathbb {r}）$的旋转最低$ k $ type系列的唯一性的猜想。
Motivated by the $(\mathfrak{g},K)$-cohomology and Dirac cohomology, we determine Dirac series of $\mathrm{GL}(n,\mathbb{H})$, and show that the spin lowest $K$-type of any Dirac series, which determines the Dirac cohomology, is unique and multiplicity-free for both $\mathrm{GL}(n,\mathbb{H})$ and $\mathrm{GL}(n,\mathbb{R})$. This verifies a conjecture about uniqueness of the spin lowest $K$-type of Dirac series for $\mathrm{GL}(n,\mathbb{R})$ proposed by Dong and Wong.
