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- W2134332192 abstract "We consider strong relative property (T) for pairs (Γ, G) where Γ acts on G. If N is a connected nilpotent Lie group and Γ is a group of automorphisms of N, we choose a finite index subgroup Γ 0 of Γ and obtain that (Γ , [Γ 0, N]) has strong relative property (T) provided Zariski-closure of Γ has no compact factor of positive dimension. We apply this to obtain the following: Let G be a connected Lie group with solvable radical R and a semisimple Levi subgroup S. If S nc denotes the product of noncompact simple factors of S and S T denotes the product of simple factors in S that have property (T), then we show that (Γ , R) or $${(Gamma S_{T}, overline{S_{T}R})}$$ has strong relative property (T) for a ’Zariski-dense’ closed subgroup Γ of S nc if and only if R = [S nc , R]. We also provide some applications to the spectral gap of π (μ) = ∫ π (g) d μ (g) where π is a certain unitary representation and μ is a probability measure." @default.
- W2134332192 created "2016-06-24" @default.
- W2134332192 creator A5076529214 @default.
- W2134332192 date "2012-07-20" @default.
- W2134332192 modified "2023-09-24" @default.
- W2134332192 title "Strong relative property (T) and spectral gap of random walks" @default.
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- W2134332192 doi "https://doi.org/10.1007/s10711-012-9756-7" @default.
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