Journal of Lie Theory

no. 1
On Kazhdan's Property (T) for Sp2(k)
Journal of Lie Theory, Volume 12 (2002) no. 1, pp. 31-39
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.
DOI: 10.5802/jolt.251
Classification: 22D10, 22E50
Keywords: symplectic group, Kazhdan's property 
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     author = {M. B. Bekka and M. 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},
     doi = {10.5802/jolt.251},
     zbl = {0996.22007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.251/}
}
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M. B. Bekka; M. Neuhauser. On Kazhdan's Property (T) for Sp2(k). Journal of Lie Theory, Volume 12 (2002) no. 1, pp. 31-39. doi: 10.5802/jolt.251

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