Relations in Twisted Quantum K-Rings

2024/06/03 by Huq-Kuruvilla, Irit · 2 citations
#14N35 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2406.00916

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.

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• Towards small quantum Chern character
• Relativistic Toda lattice and equivariant K-homology of affine Grassmannian

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