Relations in Twisted Quantum K-Rings
| Autor: | Huq-Kuruvilla, Irit |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We introduce twisted quantum $K$-rings, defined via twisted $K$-theoretic Gromov-Witten invariants. We develop a toolkit for computing relations by adapting some results about ordinary quantum K rings to our setting, and discuss some applications, including Ruan-Zhang's quantum $K$-theory with level structure, and complete intersections inside projective space, confirming some predictions coming from physics. In addition, we formulate a ring-theoretic abelian/non-abelian correspondence conjecture, relating the quantum K-ring of a GIT quotient $X//G$ to a certain twist of the quantum K-ring of $X//T$, the quotient by the maximal torus. We prove this conjecture for the case of Grassmanians, and use this to give another proof of the Whitney relations of Mihalcea-Gu-Sharpe-Zhou. Comment: 26 pages |
| Databáze: | arXiv |
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