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Kazhdan Set

Let G be a discrete group. A finite subset Q subset G is a Kazhdan set if there is an epsilon>0 such that every unitary group representation of G having a unit vector v with

||pi(g)v-v||<epsilon

for every g in Q has a nonzero invariant vector. A group has Kazhdan's property (T) if and only if it has a Kazhdan set.

See also

Group Representation, Kazhdan's Property (T), Unitary

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References

Bekka, B.; de la Harpe, P.; and Valette, A. Kazhdan's Property (T). Cambridge, England: Cambridge University Press, 2008.

Cite this as:

Weisstein, Eric W. "Kazhdan Set." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/KazhdanSet.html

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