Geodesic
On the Decomposition of a Representation of SOn When Restricted to SOn-1
Canadian journal of mathematics, Tome 44 (1992) no. 5, pp. 974-1002

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

Let k be a local field, with char(k) ≠ 2. A quadratic space V over k is a finite dimensional vector space together with a non-degenerate quadratic form Q: V → k.The special orthogonal group SO(V) consists of all linear maps T: V → V which satisfy: Q(Tv) = Q(v) for all ν and det T = 1. 
Gross, Benedict H.; Prasad, Dipendra. On the Decomposition of a Representation of SOn When Restricted to SOn-1. Canadian journal of mathematics, Tome 44 (1992) no. 5, pp. 974-1002. doi: 10.4153/CJM-1992-060-8
@article{10_4153_CJM_1992_060_8,
     author = {Gross, Benedict H. and Prasad, Dipendra},
     title = {On the {Decomposition} of a {Representation} of {SOn} {When} {Restricted} to {SOn-1}},
     journal = {Canadian journal of mathematics},
     pages = {974--1002},
     year = {1992},
     volume = {44},
     number = {5},
     doi = {10.4153/CJM-1992-060-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-060-8/}
}
TY  - JOUR
AU  - Gross, Benedict H.
AU  - Prasad, Dipendra
TI  - On the Decomposition of a Representation of SOn When Restricted to SOn-1
JO  - Canadian journal of mathematics
PY  - 1992
SP  - 974
EP  - 1002
VL  - 44
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-060-8/
DO  - 10.4153/CJM-1992-060-8
ID  - 10_4153_CJM_1992_060_8
ER  - 
%0 Journal Article
%A Gross, Benedict H.
%A Prasad, Dipendra
%T On the Decomposition of a Representation of SOn When Restricted to SOn-1
%J Canadian journal of mathematics
%D 1992
%P 974-1002
%V 44
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-060-8/
%R 10.4153/CJM-1992-060-8
%F 10_4153_CJM_1992_060_8

[A] Arthur, J., Lectures on automorphic L-functions. L-functions and arithmetic, London Math. Soc. Lecture Notes. 153(1991), 1–21. Google Scholar

[B-Z] Bernstein, J. and Zelevinsky, A., Representations of the group GL(AI,F) where F is a non-archimedean local field, Usp. Nat. Nauk. 31(1976), 5–70. Google Scholar

[Bo] Borel, A., Automorphic L-functions, Proceedings of Symposia in Pure Math. (2). 33(1979), 27–61. Google Scholar

[C-S] Casselman, W. and Shalika, J., The unramified principal series of p-adic groups, Compositio Math.. 41(1980), 207–231. Google Scholar

[De] Deligne, P., Les constants locales de V équation fonctionelle de la fonction Ld'Artin d'une representation orthogonale, Invent. Math.. 35(1976), 299–316. Google Scholar

[D] Dixmier, J., Representations intégrables du groupe de de Sitter, Bull. Soc. Math. France 89(1961), 9–41 . Google Scholar

[F] Flath, D., Decomposition of representations into tensor products, Proc. of Symposia in Pure Math. (1) 33(1979), 179–184. Google Scholar

[G-K] Gelfand, I.M. and Kazhdan, D.A., Representations of GLn(K), Lie groups and their representations, Halstead Press, 1975. Google Scholar

[Gr-P] Gross, B. H. and Prasad, D., Test vectors for invariant forms, Math. Ann. 291(1991), 343 355. Google Scholar

[Gr] Gross, B. H., L-functions at the central critical point. Google Scholar

[Hi] Hirai, T., On irreducible representations of the Lorentz group ofn-th order, Proc. Japan Adad. 38(1962), 258 262. Google Scholar

[H-Kl] Harris, M. and Kudla, S., Arithmetic automorphic forms for the non-holomorphic discrete series of Sp(2), Duke Math. J. 66(1992), 59 121. Google Scholar

[H-K2] Harris, M. and Kudla, S., The central critical value of a triple product L-function, Annals of Mathematics 133(1991), 605 672. Google Scholar

[Kn] Knapp, A. W., Representation theory of semisimple groups, Princeton Univ. Press, 1986. Google Scholar

[Ks] Kostant, B., On Whittaker vectors and representation theory, Invent. Math. 48(1978), 101 184. Google Scholar

[K] Kottwitz, R., Stable trace formula: cuspidal tempered terms, Duke Math. J. 51(1984), 611 650. Google Scholar

[Li] Li, J.-S., Theta lifting for unitary representations with non-zero cohomology, Duke Math. J. 61(1990), 913 937. Google Scholar

[M] Martens, S., The characters of the holomorphic discrete series, Proc. Nat. Acad. Sci. USA, 72(1975), 3275 3276. Google Scholar

[PI] Prasad, D., Trilinear forms for representations of GL(2) and local epsilon factors, Compositio 75(1990), 1 46. Google Scholar

[P2] Prasad, D., Invariant forms for representations of GL(2) over a local field, American Journal of Math., (1992). Google Scholar

[R] Rallis, S.. Personal communication. Google Scholar

[Ro] Rodier, F., Modles de Whittaker des representations admissibles des groupes reductives p-adiques quasidploys. Google Scholar

[S] Schmid, W., Representations of semi-simple Lie groups, London Math. Soc. Lecture Notes 34(1979), 185 235. Google Scholar

[Sa] Saito, H., On TunnelVs Theorem on Characters of GL(2). Google Scholar

[Se] Serre, J. P., A course in arithmetic, Springer GTM 7, 1973. Google Scholar

[Sh] Shahidi, F., A proof of Langlands conjecture on Plancherel measures; Complementary series for p-adic groups, Annals of Math. 132(1990), 273 330. Google Scholar

[Sk] Shalika, J., The multiplicity one theoremfor GL(«), Annals of Math. 100(1974), 171 193. Google Scholar

[Ta] Tate, J., Number theoretic background, Proc. of Symposia in Pure Math. (2) 33(1979), 3 26. Google Scholar

[Ta] Tunnell, J., Local epsilon factors and characters of GL(2), Amer. Jour. Math. 105(1983), 1277 1308. Google Scholar

[V] Vogan, D., The local Langlands conjecture. Google Scholar

[W] Waldspurger, J. L., Sur les valeurs de certaines fonctions L automorphes en leur centre de symtrie, Compositio Math. 54(1985), 173 242. Google Scholar

[Z] Zelobenko, D. P., Compact Lie groups and their representations, Translations of Mathematical Monographs, AMS 40(1973). Google Scholar

Cité par Sources :