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In the case where $|Q(s,t)|\\equiv 1$, the $Q$-deformed commutation relations describe a generalized statistics studied "},"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":"1603.03075","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-08T09:39:05Z","cross_cats_sorted":["math.MP","math.OA"],"title_canon_sha256":"1f254bc363377fa6aa0b19279b6ba0749f66acf065378673d625c344be619dd5","abstract_canon_sha256":"7d80f5d12db20a314d6496994031f27d4f3437c9f2ba5dd2cf43a1f245c743f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:03.055377Z","signature_b64":"9bhDZbh0SnrT6MEjmRLd/INZFOX8ew2rQg6Pk3GZqS5yJ5abGBQXYHE/Z390pXv3xW299y3XVB/pbAAVxKF1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d38c10c2eb0bfe93fec23b3ab774df0f01db1657aabef72f6b07f1994a1ac750","last_reissued_at":"2026-05-18T00:39:03.054835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:03.054835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fock representations of $Q$-deformed commutation relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Eugene Lytvynov, Janusz Wysocza\\'nski, Marek Bo\\.zejko","submitted_at":"2016-03-08T09:39:05Z","abstract_excerpt":"We consider Fock representations of the $Q$-deformed commutation relations $$\\partial_s\\partial^\\dag_t=Q(s,t)\\partial_t^\\dag\\partial_s+\\delta(s,t), \\quad s,t\\in T.$$ Here\n  $T:=\\mathbb R^d$ (or more generally $T$ is a locally compact Polish space), the function $Q:T^2\\to \\mathbb C$ satisfies $|Q(s,t)|\\le1$ and $Q(s,t)=\\overline{Q(t,s)}$, and $$\\int_{T^2}h(s)g(t)\\delta(s,t)\\,\\sigma(ds)\\sigma(dt):=\\int_T h(t)g(t)\\,\\sigma(dt),$$\n  $\\sigma$ being a fixed reference measure on $T$. 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