Greenberg-Shalom's Commensurator Hypothesis and Applications Article Swipe
Related Concepts
Shalom
Automorphism group
Mathematics
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Pure mathematics
Philosophy
Automorphism
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Mathematical analysis
Nic Brody
,
David E. Fisher
,
Mahan Mj
,
Wouter van Limbeek
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2308.07785
· OA: W4385890216
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2308.07785
· OA: W4385890216
We discuss many surprising implications of a positive answer to a question raised in some cases by Greenberg in the $`70$s and more generally by Shalom in the early $2000$s. We refer to this positive answer as the Greenberg-Shalom hypothesis. This hypothesis then says that any infinite discrete subgroup of a semisimple Lie group with dense commensurator is a lattice in a product of some factors. For some applications it is natural to extend the hypothesis to cover semisimple algebraic groups over other fields as well.
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