Geodesic
Remarks on Certain Metaplectic Groups
Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 488-496

Voir la notice de l'article provenant de la source Cambridge University Press

We study metaplectic coverings of the adelized group of a split connected reductive group $G$ over a number field $F$ . Assume its derived group ${G}'$ is a simply connected simple Chevalley group. The purpose is to provide some naturally defined sections for the coverings with good properties which might be helpful when we carry some explicit calculations in the theory of automorphic forms on metaplectic groups. Specifically, we 1. construct metaplectic coverings of $G(\mathbb{A})$ from those of ${G}'\,(\mathbb{A})$ ; 2. for any non-archimedean place $v$ , show the section for a covering of $G\,({{F}_{v}})$ constructed from a Steinberg section is an isomorphism, both algebraically and topologically in an open subgroup of $G\,({{F}_{v}})$ ; 3. define a global section which is a product of local sections on a maximal torus, a unipotent subgroup and a set of representatives for the Weyl group.
DOI : 10.4153/CMB-1998-064-1
Mots-clés : 20G10, 11G75 
Sun, Heng. Remarks on Certain Metaplectic Groups. Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 488-496. doi: 10.4153/CMB-1998-064-1
@article{10_4153_CMB_1998_064_1,
     author = {Sun, Heng},
     title = {Remarks on {Certain} {Metaplectic} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {488--496},
     year = {1998},
     volume = {41},
     number = {4},
     doi = {10.4153/CMB-1998-064-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-064-1/}
}
TY  - JOUR
AU  - Sun, Heng
TI  - Remarks on Certain Metaplectic Groups
JO  - Canadian mathematical bulletin
PY  - 1998
SP  - 488
EP  - 496
VL  - 41
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-064-1/
DO  - 10.4153/CMB-1998-064-1
ID  - 10_4153_CMB_1998_064_1
ER  - 
%0 Journal Article
%A Sun, Heng
%T Remarks on Certain Metaplectic Groups
%J Canadian mathematical bulletin
%D 1998
%P 488-496
%V 41
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-064-1/
%R 10.4153/CMB-1998-064-1
%F 10_4153_CMB_1998_064_1

[1] 1. Kazhdan, D. A. and Patterson, S. J., Metaplectic forms. Inst. Hautes Ètudes Sci. Publ. Math. 59 (1984), 35–142. Google Scholar

[2] 2. Kubota, T., On automorphic functions and the reciprocity law in a number field. Kinokuniya Book-Store Co., Ltd., Tokyo, 1969. Google Scholar

[3] 3. Matsumoto, H., Sur les sous-groupes arithmétiques des groupes semi-simples déployés. Ann. Sci. Ècole Norm. Sup. Sér. 4 2 (1969), 1–62. Google Scholar

[4] 4. Moeglin, C. and Waldspurger, J. L., Décomposition spectrale et séries d’Eisenstein (Une paraphrase de l’Écriture). Progr. Math. 113, Birkhäuse Verlag, 1993. Google Scholar

[5] 5. Moore, C., Group extensions of p-adic and adelic linear groups. Inst. Hautes Ètudes Sci. Publ. Math. 35 (1968), 157–222. Google Scholar

[6] 6. Nagao, H., The extensions of topological groups. Osaka J. Math. 1 (1949), 36–42. Google Scholar

[7] 7. Steinberg, R., Générateurs, relations et revĚtements de groupes algébriques. In: Colloque de Bruxelles, 1962, 113–127. Google Scholar

[8] 8. Steinberg, R., Lectures on Chevalley groups. Yale University, 1967. Google Scholar

Cité par Sources :