Geodesic
On Kazhdan's Property (T) for Sp2(k)
M. B. Bekka1 ; Markus Neuhauser2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
1Dép. des Mathématiques, Université de Metz, Ile du Saulcy, 57045 Metz, France
2Zentrum Mathematik, Technische Universität, Arcisstrasse 21, 80290 München, Germany
3The aim of this note is to give a new and elementary proof of Kazhdan's Property (T) for Sp
4(
5), the symplectic group on 4 variables, for any local field
6. The crucial step is the proof that the Dirac measure δ
7at 0 is the unique mean on the Borel subsets of the second symmetric power S
8) of
9which is invariant under the natural action of SL
10). In the case where
11has characteristic 2, we observe that this is no longer true if S
12) is replaced by its dual, the space of the symmetric bilinear forms on
13.
14[
Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 31-39 
M. B. Bekka; Markus Neuhauser. On Kazhdan's Property (T) for Sp2(k). Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 31-39. http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a2/
@article{JOLT_2002_12_1_a2,
     author = {M. B. Bekka and Markus Neuhauser},
     title = {On {Kazhdan's} {Property} {(T)} for {Sp\protect\textsubscript{2}(k)}},
     journal = {Journal of Lie Theory},
     pages = {31--39},
     year = {2002},
     volume = {12},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a2/}
}
TY  - JOUR
AU  - M. B. Bekka
AU  - Markus Neuhauser
TI  - On Kazhdan's Property (T) for Sp2(k)
JO  - Journal of Lie Theory
PY  - 2002
SP  - 31
EP  - 39
VL  - 12
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a2/
ID  - JOLT_2002_12_1_a2
ER  - 
%0 Journal Article
%A M. B. Bekka
%A Markus Neuhauser
%T On Kazhdan's Property (T) for Sp2(k)
%J Journal of Lie Theory
%D 2002
%P 31-39
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a2/
%F JOLT_2002_12_1_a2

Voir la notice de l'article provenant de la source Heldermann Verlag

The aim of this note is to give a new and elementary proof of Kazhdan's Property (T) for Sp2(k), the symplectic group on 4 variables, for any local field k. The crucial step is the proof that the Dirac measure δ0 at 0 is the unique mean on the Borel subsets of the second symmetric power S2(k2) of k2 which is invariant under the natural action of SL2(k). In the case where k has characteristic 2, we observe that this is no longer true if S2(k2) is replaced by its dual, the space of the symmetric bilinear forms on k2.