Quantum K Whitney relations for partial flag varieties
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929592003985408 |
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| author | Gu, Wei Mihalcea, Leonardo C. Sharpe, Eric Xu, Weihong Zhang, Hao Zou, Hao |
| author_facet | Gu, Wei Mihalcea, Leonardo C. Sharpe, Eric Xu, Weihong Zhang, Hao Zou, Hao |
| contents | In a recent paper, we stated conjectural presentations for the equivariant quantum K ring of partial flag varieties, motivated by physics considerations. In this companion paper, we analyze these presentations mathematically. We start by proving a Nakayama type result for quantum K theory: if the conjectured set of relations deforms a complete set of relations of the classical K theory ring, then they must form a complete set of relations for the quantum K ring. We prove the conjectured presentation in the case of the incidence varieties, and we show that if a quantum K divisor axiom holds (as conjectured by Buch and Mihalcea), then the conjectured presentation also holds for the complete flag variety. Finally, we briefly revisit the change of variables relating the mathematics and physics presentations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03826 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum K Whitney relations for partial flag varieties Gu, Wei Mihalcea, Leonardo C. Sharpe, Eric Xu, Weihong Zhang, Hao Zou, Hao Algebraic Geometry High Energy Physics - Theory Combinatorics Primary 14M15, 14N35, 81T60, Secondary 05E05 In a recent paper, we stated conjectural presentations for the equivariant quantum K ring of partial flag varieties, motivated by physics considerations. In this companion paper, we analyze these presentations mathematically. We start by proving a Nakayama type result for quantum K theory: if the conjectured set of relations deforms a complete set of relations of the classical K theory ring, then they must form a complete set of relations for the quantum K ring. We prove the conjectured presentation in the case of the incidence varieties, and we show that if a quantum K divisor axiom holds (as conjectured by Buch and Mihalcea), then the conjectured presentation also holds for the complete flag variety. Finally, we briefly revisit the change of variables relating the mathematics and physics presentations. |
| title | Quantum K Whitney relations for partial flag varieties |
| topic | Algebraic Geometry High Energy Physics - Theory Combinatorics Primary 14M15, 14N35, 81T60, Secondary 05E05 |
| url | https://arxiv.org/abs/2310.03826 |