TY - JOUR
T1 - Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity
AU - Shalom, Yehuda
AU - Willis, George A.
N1 - Funding Information:
The authors thank Gregory Margulis and Robert Zimmer for their input to the manuscript. Deep and special gratitude goes to Gopal Prasad for the wealth of crucial information he provided during the work on Section 7.2, and to Andrei Rap-inchuk who has read a previous version of this section with great care, pointing out many improvements. The first author acknowledges the support of the ISF and NSF through grants 500/05 and DMS-0701639, DMS-1007227 resp. The second author acknowledges the ARC support through grants LX0667119 and DP0984342.
PY - 2013/10
Y1 - 2013/10
N2 - The paper establishes a substantial number of cases of a conjecture regarding commensurated subgroups of S-arithmetic groups made by Margulis and Zimmer in the late 1970s. New results in the structure theory of totally disconnected groups are established along the way and are of independent interest. Other ideas in the argument motivate a sweeping conjecture, presented in the last section of the paper, which naturally unifies in an adelic setting deep results and fundamental conjectures in the rigidity theory of arithmetic groups.
AB - The paper establishes a substantial number of cases of a conjecture regarding commensurated subgroups of S-arithmetic groups made by Margulis and Zimmer in the late 1970s. New results in the structure theory of totally disconnected groups are established along the way and are of independent interest. Other ideas in the argument motivate a sweeping conjecture, presented in the last section of the paper, which naturally unifies in an adelic setting deep results and fundamental conjectures in the rigidity theory of arithmetic groups.
UR - http://www.scopus.com/inward/record.url?scp=84884412165&partnerID=8YFLogxK
U2 - 10.1007/s00039-013-0236-5
DO - 10.1007/s00039-013-0236-5
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AN - SCOPUS:84884412165
SN - 1016-443X
VL - 23
SP - 1631
EP - 1683
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 5
ER -