Geodesic
Embeddings of L-Groups
Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 513-558

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

To a real reductive group G there is attached a family of (real) groups, each of lower dimension but sharing Cartan subgroups with G (cf. [8]). The purpose of these groups is to provide “building blocks” (in a specific sense (cf. [11])) for analysis on G. Their définition is via an L-group construction; the connected component of the identity, LH 0, in the L-group of such a group H is naturally a subgroup of LG 0 but the requirement that H “share” Cartan subgroups with G precludes defining LH the full L-group of H, as a subgroup of LG. Nevertheless, the principle of functoriality in the L-group suggests that the embeddings of LH in LG will play a role in analysis. In this paper, we study the embeddings of LH in LG in order to resolve a problem about the normalization of orbital integrals. 
Shelstad, D. Embeddings of L-Groups. Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 513-558. doi: 10.4153/CJM-1981-044-4
@article{10_4153_CJM_1981_044_4,
     author = {Shelstad, D.},
     title = {Embeddings of {L-Groups}},
     journal = {Canadian journal of mathematics},
     pages = {513--558},
     year = {1981},
     volume = {33},
     number = {3},
     doi = {10.4153/CJM-1981-044-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-044-4/}
}
TY  - JOUR
AU  - Shelstad, D.
TI  - Embeddings of L-Groups
JO  - Canadian journal of mathematics
PY  - 1981
SP  - 513
EP  - 558
VL  - 33
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-044-4/
DO  - 10.4153/CJM-1981-044-4
ID  - 10_4153_CJM_1981_044_4
ER  - 
%0 Journal Article
%A Shelstad, D.
%T Embeddings of L-Groups
%J Canadian journal of mathematics
%D 1981
%P 513-558
%V 33
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-044-4/
%R 10.4153/CJM-1981-044-4
%F 10_4153_CJM_1981_044_4

[1] 1. Arthur, J., On the invariant distributions associated to weighted orbital integrals, preprint. Google Scholar

[2] 2. Borel, A., Linear algebraic groups (Benjamin, 1969). Google Scholar

[3] 3. Borel, A., Automorphic L-functions, Proc. Sympos. Pure Math. 33 Amer. Math. Soc. (1979), 27–61. Google Scholar

[4] 4. Bourbaki, N., Groupes et algèbres de Lie, Chs. 4, 5, 6 (Hermann, 1968). Google Scholar

[5] 5. Freudenthal, H. and de Vries, H., Linear Lie groups (Academic Press, 1969). Google Scholar

[6] 6. Harish-Chandra, , Harmonie analysis on real reductive Lie groups I, J. Funct. Analysis 19 (1975), 104–204. Google Scholar

[7] 7. Langlands, R., On the classification of irreducible representations of real algebraic groups, Notes, IAS. Google Scholar

[8] 8. Langlands, R., Stable conjugacy; definition and lemmas, Can. J. Math. 31 (1979), 700–725. Google Scholar

[9] 9. Shelstad, D., Characters and inner forms of a quasi-split group overR, Compositio Math. 39 (1979), 11–45. Google Scholar

[10] 10. Shelstad, D., Orbital integrals and a family of groups attached to a real reductive group, Ann. Scient. Ec. Norm. Sup., 4e série, t. 12 (1979), 1–31. Google Scholar

[11] 11. Shelstad, D., Notes on L-indistinguishability, Proc. Sympos. Pure Math. 33 Amer. Math. Soc. (1979), 193–203. Google Scholar

[12] 12. Steinberg, R., Regular elements of semi-simple algebraic groups, Publ. Math. I.H.E.S. 25 (1965), 49–80. Google Scholar

Cité par Sources :