Relative Property (T) for Nilpotent Subgroups
Documenta mathematica, Tome 23 (2018), pp. 353-382
We show that relative Property (T) for the abelianization of a nilpotent normal subgroup implies relative Property (T) for the subgroup itself. This and other results are a consequence of a theorem of independent interest, which states that if H is a closed subgroup of a locally compact group G, and A is a closed subgroup of the center of H, such that A is normal in G, and (G/A,H/A) has relative Property (T), then (G,H(1)) has relative Property (T), where H(1) is the closure of the commutator subgroup of H. In fact, the assumption that A is in the center of H can be replaced with the weaker assumption that A is abelian and every H-invariant finite measure on the unitary dual of A is supported on the set of fixed points.
Classification :
22D10
Mots-clés : relative Property (T), nilpotent subgroup, almost-invariant vector, fibered tensor product
Mots-clés : relative Property (T), nilpotent subgroup, almost-invariant vector, fibered tensor product
@article{10_4171_dm_621,
author = {Indira Chatterji and Dave Witte Morris and Riddhi Shah},
title = {Relative {Property} {(T)} for {Nilpotent} {Subgroups}},
journal = {Documenta mathematica},
pages = {353--382},
year = {2018},
volume = {23},
doi = {10.4171/dm/621},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/621/}
}
Indira Chatterji; Dave Witte Morris; Riddhi Shah. Relative Property (T) for Nilpotent Subgroups. Documenta mathematica, Tome 23 (2018), pp. 353-382. doi: 10.4171/dm/621
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