Remarks on certain metaplectic groups

Canadian mathematical bulletin

关键词: Injectivity;    ${cal C}^1$-maps;    polynomial maps;    Jacobian Conjecture;    Mountain Pass;   

DOI  :  10.4153/CMB-1998-064-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We study metaplectic coverings of the adelized group of a splitconnected reductive group $G$ over a number field $F$. Assume itsderived group $G'$ is a simply connected simple Chevalleygroup. The purpose is to provide some naturally defined sectionsfor the coverings with good properties which might be helpful whenwe carry some explicit calculations in the theory of automorphicforms on metaplectic groups. Specifically, we egin{enumerate}item construct metaplectic coverings of $G({Bbb A})$ from thoseof $G'({Bbb A})$; item for any non-archimedean place $v$, show the section for acovering of $G(F_{v})$ constructed from a Steinberg section is anisomorphism, both algebraically and topologically in an opensubgroup of $G(F_{v})$; item define a global section which is a product of local sectionson a maximal torus, a unipotent subgroup and a set ofrepresentatives for the Weyl group.

【 授权许可】

Unknown