Quantum $K$-theoretic Whitney relations for type $C$ flag manifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917173592588288 |
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| author | Kouno, Takafumi |
| author_facet | Kouno, Takafumi |
| contents | We study relations of $λ_{y}$-classes associated to tautological bundles over the flag manifold of type $C$ in the quantum $K$-ring. These relations are called the quantum $K$-theoretic Whitney relations. The strategy of the proof of the quantum $K$-theoretic Whitney relations is based on the method of semi-infinite flag manifolds and the Borel-type presentation. In addition, we observe that the quantum $K$-theoretic Whitney relations give a complete set of the defining relations of the quantum $K$-ring. This gives a presentation of the quantum $K$-ring of the flag manifold of type $C$, called the Whitney-type presentation, as a quotient of a polynomial ring, different from the Borel-type presentation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_23224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum $K$-theoretic Whitney relations for type $C$ flag manifolds Kouno, Takafumi Quantum Algebra Algebraic Geometry Combinatorics K-Theory and Homology Representation Theory Primary: 14M15, Secondary: 14N15, 14N35, 05E10 We study relations of $λ_{y}$-classes associated to tautological bundles over the flag manifold of type $C$ in the quantum $K$-ring. These relations are called the quantum $K$-theoretic Whitney relations. The strategy of the proof of the quantum $K$-theoretic Whitney relations is based on the method of semi-infinite flag manifolds and the Borel-type presentation. In addition, we observe that the quantum $K$-theoretic Whitney relations give a complete set of the defining relations of the quantum $K$-ring. This gives a presentation of the quantum $K$-ring of the flag manifold of type $C$, called the Whitney-type presentation, as a quotient of a polynomial ring, different from the Borel-type presentation. |
| title | Quantum $K$-theoretic Whitney relations for type $C$ flag manifolds |
| topic | Quantum Algebra Algebraic Geometry Combinatorics K-Theory and Homology Representation Theory Primary: 14M15, Secondary: 14N15, 14N35, 05E10 |
| url | https://arxiv.org/abs/2512.23224 |