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Here $T=(C^*)^n\\times C^*$. The torus $(C^*)^n$ acts on $T^* Gr$ in the standard way and the last factor $C^*$ acts by multiplication on fibers of the bundle. We express this fundamental class as a sum $Y_I$ of the Yangian $Y(gl_2)$ weight functions $(W_J)_J$. We describe a relation of $Y_I$ with the double Schur polynomial $[S_I]$.\n  A modified ver"},"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":"1204.4961","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-23T01:54:19Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"1b60ebcbf646116ca0e724838379ead58a7d3acd69774b32e2714eda4876fe5e","abstract_canon_sha256":"712aa9abb5970b145d337a981d02f2ee97e0743608296600c8481ab4d20b8274"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:38.525449Z","signature_b64":"ujb3J7CckfyQJJgFq8T4Qb5kdy2EGzknsJMJEz931pMYzSzBkzZcYD66QUhxzQqcln8zVGEoBcsiuaZ2XlGBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1d810f66aa55bf06258125cc34fcf9c4963b72868734c510205a6d05eb684bb","last_reissued_at":"2026-05-18T03:04:38.524540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:38.524540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.AG","authors_text":"A. Varchenko, R. Rimanyi, V. Tarasov","submitted_at":"2012-04-23T01:54:19Z","abstract_excerpt":"We consider the conormal bundle of a Schubert variety $S_I$ in the cotangent bundle $T^* Gr$ of the Grassmannian $Gr$ of $k$-planes in $C^n$. This conormal bundle has a fundamental class ${\\kappa_I}$ in the equivariant cohomology $H^*_{T}(T^* Gr)$. Here $T=(C^*)^n\\times C^*$. The torus $(C^*)^n$ acts on $T^* Gr$ in the standard way and the last factor $C^*$ acts by multiplication on fibers of the bundle. We express this fundamental class as a sum $Y_I$ of the Yangian $Y(gl_2)$ weight functions $(W_J)_J$. 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