Journal article
Non-vanishing unitary cohomology of low-rank integral special linear groups
- Abstract:
- We construct explicit finite-dimensional orthogonal representations πN of SLN (Z) for N ∈ {3, 4} all of whose invariant vectors are trivial, and such that HN−1 (SLN (Z), πN ) is non-trivial. This implies that for N as above, the group SLN (Z) does not have property (TN−1) of Bader–Sauer and therefore is not (N −1)-Kazhdan in the sense of De Chiffre–Glebsky–Lubotzky–Thom, both being higher versions of Kazhdan’s property T.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 653.6KB, Terms of use)
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- Publisher copy:
- 10.1093/imrn/rnaf230
Authors
+ European Research Council
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- Funder identifier:
- https://ror.org/0472cxd90
- Grant:
- 850930
- Publisher:
- Oxford University Press
- Journal:
- International Mathematics Research Notices More from this journal
- Volume:
- 2025
- Issue:
- 15
- Pages:
- rnaf230
- Publication date:
- 2025-08-06
- Acceptance date:
- 2025-07-13
- DOI:
- EISSN:
-
1687-0247
- ISSN:
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1073-7928
- Language:
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English
- Pubs id:
-
2243432
- Local pid:
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pubs:2243432
- Deposit date:
-
2025-07-13
Terms of use
- Copyright holder:
- Brück et al.
- Copyright date:
- 2025
- Rights statement:
- © The Author(s) 2025. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
- Licence:
- CC Attribution (CC BY)
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