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To each Caloger-Moser two-sided cell is associated a Calogero-Moser family, while to each Calogero-Moser left cell is associated a Calogero-Moser cellular representation. We study properties of these objects and we conjecture that, whenever the reflection group is real (i.e. is a Coxeter group), these notions coincide with the one of Kazhdan-Lusztig left, right and two-sid"},"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":"1302.2720","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-12T07:18:39Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"cb37b2b9e22786e6a2d0d34ca46b41dcffe384712c9e9f788e7f0c3ae874f676","abstract_canon_sha256":"e550c85f6a3075209a821eccaf5762a6b506254a1b4e9b37e2375e607df1d5cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:51.129534Z","signature_b64":"hM9WVo5wvtHWBq4cKh9ncYARBxyoq4XE6eBBjX1VAe2FSe77QG2BeH27I+/2sk07qHCLibma4PyjMB7KnZwhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38c17a1d1e13c70568ab2343f23559374e224542fc23fa9329b118afe499ae56","last_reissued_at":"2026-05-18T03:33:51.128755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:51.128755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cellules de Calogero-Moser","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"C\\'edric Bonnaf\\'e, Rapha\\\"el Rouquier","submitted_at":"2013-02-12T07:18:39Z","abstract_excerpt":"Using the representation theory of Cherednik algebras at t=0 and a Galois covering of the Calogero-Moser space, we define the notions of left, right and two-sided Calogero-Moser cells for any finite complex reflection group. 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