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arXiv · 2406.00916

Relations in Twisted Quantum K-Rings

Irit Huq-Kuruvilla
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Abstract

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 in that case. We work in the generality of permutation-equivariant invariants.

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Irit Huq-Kuruvilla. 2024-06-03. Relations in Twisted Quantum K-Rings. https://arxiv.org/abs/2406.00916

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