TY - JOUR
T1 - Invariant random subgroups over non-Archimedean local fields
AU - Gelander, Tsachik
AU - Levit, Arie
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/12/1
Y1 - 2018/12/1
N2 - Let G be a higher rank semisimple linear algebraic group over a non-Archimedean local field. The simplicial complexes corresponding to any sequence of pairwise non-conjugate irreducible lattices in G are Benjamini–Schramm convergent to the Bruhat–Tits building. Convergence of the relative Plancherel measures and normalized Betti numbers follows. This extends the work (Abert et al. in Ann Math 185(3):711–790, 2017) from real Lie groups to linear groups over arbitrary local fields. Along the way, various results concerning Invariant Random Subgroups and in particular a variant of the classical Borel density theorem are also extended.
AB - Let G be a higher rank semisimple linear algebraic group over a non-Archimedean local field. The simplicial complexes corresponding to any sequence of pairwise non-conjugate irreducible lattices in G are Benjamini–Schramm convergent to the Bruhat–Tits building. Convergence of the relative Plancherel measures and normalized Betti numbers follows. This extends the work (Abert et al. in Ann Math 185(3):711–790, 2017) from real Lie groups to linear groups over arbitrary local fields. Along the way, various results concerning Invariant Random Subgroups and in particular a variant of the classical Borel density theorem are also extended.
UR - http://www.scopus.com/inward/record.url?scp=85055753447&partnerID=8YFLogxK
U2 - 10.1007/s00208-018-1767-8
DO - 10.1007/s00208-018-1767-8
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AN - SCOPUS:85055753447
SN - 0025-5831
VL - 372
SP - 1503
EP - 1544
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3-4
ER -