Rigidity of commensurators and irreducible lattices

By Yehuda Shalom. 2000

246 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/556dba07927c4c7b15dd3578da52cee32f580de1

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Citations in the corpus

Isometric Group Actions on Banach Spaces and Representations Vanishing at Infinity (2006, background): “N = Ni × Q j6=i Nj; by [ Sha , Proposition 3.2] (which uses second countability), Q j6=i Nj has an invariant vector by π ◦ p, so that for every j 6= i, Nj has an invariant vector by π ◦ p.”
A SURVEY OF MEASURED GROUP THEORY (2009, unknown): “Shalom’s [110] provides a completely geometric explanation).”
Simplicity and superrigidity of twin building lattices (2006, background): “Shalom’s condition [67] is the following.”
Property (T) for noncommutative universal lattices (2008, background): “argument we just sketched proves property (T) not only for the group ELn(R) (under the additional assumption m ≥ 5 or n ≥ 9) but for an explicit ﬁnitely presented cover of it. It was proved by Shalom [Sh2] that every discrete group with (T) has a ﬁnitely presented cover with (T); however, to the bes”
On a class of II_1 factors with at most one Cartan subalgebra II (2008, background): “the property (HH)+ for G= SO(n,1) (n≥2) and SU(n,1). It follows from Theorem 3 in [BV] that every non-trivial irreducible representation of Gis non-amenable. Since Gdoes not have the property (T), by [Sh1], there is a non-trivial irreducible representation with an unbounded 1-cocycle. But, by [Sh2],”
Cocycle Superrigidity for Profinite Actions of Property (T) Groups (2008, background): “ let Γ be a countable group such that Rt is induced by a free action of Γ. Since Rhas property (T), Rt has property (T), hence Γ has property (T) ([Fu1]). Also, recall that by a theorem of Y. Shalom ([Sh2]), any property (T) group is the quotient of a ﬁnitely presented, property (T) group. Assume by”
Introduction to Arithmetic Groups (2001, methodology): “ISBN 3-540-09972-7; MR0584623 (82j:10041) [10] G.”
RELATIVE KAZHDAN PROPERTY (2005, background): “Recall the key result, due to Shalom [Sha2, Theorem 5.5] (see also [BHV, §1.4]).”
Ideal bicombings for hyperbolic groups and applications (2003, background): “3 in [32], one deduces that there is a compact normal subgroup K / H such that the homomorphism → H=K extends to a continuous homomorphism G → H=K factoring through Gi.”
Property (T) and rigidity for actions on Banach spaces (2005, methodology): “ such an action can be viewed as an aﬃne isometric Γ-action on a ucus Banach space B. It therefore suﬃces to apply the splitting theorem to the induced G-action on an induced space Lp(G/Γ,B) (compare [Sh] for the Hilbertian case). The goal of this section is to address the various (mostly technical)”
Isometry groups of non‐positively curved spaces: discrete subgroups (2009, background): “This follows from the current conclusion in the more restricted setting of [64] thanks to Shalom’s super-rigidity for characters [80], unless of course Gi admits (virtually) a non-zero continuous homomorphism to R (after all in the current setting we can have Gi = R).”
Limit groups as limits of free groups: compactifying the set of free groups. (2004, background): “rked groups converges to a ﬁnitely presented solvable (resp. amenable, Kazhdan-(T)) group, then all groups in this sequence are eventually solvable (resp. amenable, Kazhdan-(T)). Shalom has proved in [Sha00] that any ﬁnitely generated Kazhdan-(T) group is a quotient of a ﬁnitely presented Kazhdan-(T”
On the joint spectral radius for isometries of non-positively curved spaces and uniform growth (2018, unknown): “dean spaces however, then L(Sn) grows linearly provided L(S) > 0. This follows from the combination of Propositions9.3and1.8. Remark 3.9. In [58] V. Laorgue gave another proof of Shalom’s theorem [72] that a group without property (T) has non-trivial rst reduced cohomology. His main lemma is esse”
Cubulating small cancellation groups (2004, background): “Suppose that G had property (T), then by [ Sh ], there is an epimorphism”