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Let $G$ a non amenable countable subgroup acting on locally finite tree $X$. Assume either that the stabilizer in $G$ of every vertex of $X$ is finite or that the closure of the image of $G$ in ${\\rm Aut}(X)$ is not amenable. We show that $G$ has uncountably many infinite dimensional irreducible unitary representations $(\\pi, \\mathcal{H})$ of $G$ which are traceable, th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1806.10110","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-06-26T17:08:20Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b86bab6e0e72c7a8c80893d80c3bd7626f5a47d86c61ae50b978943ed6102c51","abstract_canon_sha256":"7422a642f2f30d04cfb5f49277701d77d53ea063664b216e532534b2e5864c46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:13.356308Z","signature_b64":"Gi3Zfx6FIjW2NBRgByg0bdx4gNdL7nDdwBsqkNbmAS9kZv5aViLiRR6aolV/LxsH9NlfN28mFFDfGiX/P6xSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da43e2088bb4d4c095457b597de497e7b7bece715d7d67bbf5b7232f6abcac14","last_reissued_at":"2026-05-18T00:12:13.355764Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:13.355764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinite characters on $GL_n(\\mathbf{Q})$, on $SL_n(\\mathbf{Z}),$ and on groups acting on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Bachir Bekka","submitted_at":"2018-06-26T17:08:20Z","abstract_excerpt":"Answering a question of J. 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