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We consider the Radon, cosine and sine transforms, $\\mathcal R_{r^\\prime, r}$, $\\mathcal C_{r^\\prime, r}$ and $\\mathcal S_{r^\\prime, r}$, from the $L^2$ space $L^2(G_{n,r}(\\bbK))$ to the space $L^2(G_{n,r^\\prime}(\\bbK))$, for $r, r^\\prime \\le n-1$. The $L^2$ spaces are decomposed into irreducible representations of $G$ with multiplicity free. We compute the spectral symbols of the transforms under 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":"0810.5257","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-10-29T12:04:08Z","cross_cats_sorted":[],"title_canon_sha256":"09beb193ea6a902d378977aed8b82c0a15c31ff4378b44d707d7b798dacf5385","abstract_canon_sha256":"bf10ff6806ce587a5ea090ffffce2f95d56a1c8bdd73ccb1604091b0c0211557"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:55.263166Z","signature_b64":"Ur9DR7mqGoq2eHWIooOXpvESASP9tnVzfH0prX6FWZPRKI9ngKBkyD7BfZfgJbOQ/iFZU5HIRzEIRvbEFh/DCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8b36d90ad1bafb836c9fad85b737a81d9d28cb805fe2f7548b170b516fea6be","last_reissued_at":"2026-05-18T03:07:55.262478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:55.262478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Radon, cosine and sine transforms on Grassmannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Genkai Zhang","submitted_at":"2008-10-29T12:04:08Z","abstract_excerpt":"Let $G_{n,r}(\\bbK)$ be the Grassmannian manifold of $k$-dimensional $\\bbK$-subspaces in $\\bbK^n$ where $\\bbK=\\mathbb R, \\mathbb C, \\mathbb H$ is the field of real, complex or quaternionic numbers. We consider the Radon, cosine and sine transforms, $\\mathcal R_{r^\\prime, r}$, $\\mathcal C_{r^\\prime, r}$ and $\\mathcal S_{r^\\prime, r}$, from the $L^2$ space $L^2(G_{n,r}(\\bbK))$ to the space $L^2(G_{n,r^\\prime}(\\bbK))$, for $r, r^\\prime \\le n-1$. The $L^2$ spaces are decomposed into irreducible representations of $G$ with multiplicity free. 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