论文标题
Chevalley Group的双重封面上的Hecke代数，$ \ Mathbb {q} _ {2} $
A Hecke Algebra on the Double Cover of a Chevalley Group Over $\mathbb{Q}_{2}$
论文作者
论文摘要
我们证明，在非线性双重封面上，某个真正的Hecke代数$ \ Mathcal {h} $的简单，简单，简单，简单连接的，Chevalley Group $ g $ abo $ \ mathbb {q} _ {2} _ {2} $承认伯恩斯坦介绍。该演示文稿有两个后果。首先，包含真正的未受到主体系列的Bernstein组件相当于$ \ Mathcal {H} $ - mod。其次，$ \ MATHCAL {H} $是线性群体$ g/z_ {2} $的iWahori-hecke代数的同构，其中$ z_ {2} $是$ g $中心的$ 2 $ torcesion。 Hecke代数的同构象征性提供了$ G $的双重封面的某些真实未受到的主系列与$ g/z_ {2} $组的iWahori-unramifiend表示形式之间的对应关系。
We prove that a certain genuine Hecke algebra $\mathcal{H}$ on the non-linear double cover of a simple, simply-laced, simply-connected, Chevalley group $G$ over $\mathbb{Q}_{2}$ admits a Bernstein presentation. This presentation has two consequences. First, the Bernstein component containing the genuine unramified principal series is equivalent to $\mathcal{H}$-mod. Second, $\mathcal{H}$ is isomorphic to the Iwahori-Hecke algebra of the linear group $G/Z_{2}$, where $Z_{2}$ is the $2$-torsion of the center of $G$. This isomorphism of Hecke algebras provides a correspondence between certain genuine unramified principal series of the double cover of $G$ and the Iwahori-unramified representations of the group $G/Z_{2}$.
