Geodesic
Elementary spherical functions on the group $SL(2,P)$ over a field~$P$, which is not locally compact, with respect to the subgroup of matrices with integral elements
Izvestiya. Mathematics , Tome 1 (1967) no. 2, pp. 349-380

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that in the space $H$ of an irreducible unitary (in the $\Pi_1$-metric) representation $T(g)$ of the group $G=SL(2,P)$ over a normed field $P$ that is not locally compact there exists a vector $y_0$ satisfying the condition $T(g)y_0=y_0$, where $g$ runs over the subgroup $G_0$ of matrices $g\in G$ with integral elements. The function $(T(g)y_0,y_0)$ is calculated; also investigated are the unitary representations of $G$ containing the identity representation $G_0$. 
@article{IM2_1967_1_2_a9,
     author = {R. S. Ismagilov},
     title = {Elementary spherical functions on the group $SL(2,P)$ over a field~$P$, which is not locally compact, with respect to the subgroup of matrices with integral elements},
     journal = {Izvestiya. Mathematics },
     pages = {349--380},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1967},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a9/}
}
TY  - JOUR
AU  - R. S. Ismagilov
TI  - Elementary spherical functions on the group $SL(2,P)$ over a field~$P$, which is not locally compact, with respect to the subgroup of matrices with integral elements
JO  - Izvestiya. Mathematics 
PY  - 1967
SP  - 349
EP  - 380
VL  - 1
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a9/
LA  - en
ID  - IM2_1967_1_2_a9
ER  - 
%0 Journal Article
%A R. S. Ismagilov
%T Elementary spherical functions on the group $SL(2,P)$ over a field~$P$, which is not locally compact, with respect to the subgroup of matrices with integral elements
%J Izvestiya. Mathematics 
%D 1967
%P 349-380
%V 1
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a9/
%G en
%F IM2_1967_1_2_a9
R. S. Ismagilov. Elementary spherical functions on the group $SL(2,P)$ over a field~$P$, which is not locally compact, with respect to the subgroup of matrices with integral elements. Izvestiya. Mathematics , Tome 1 (1967) no. 2, pp. 349-380. http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a9/