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arXiv · 1804.04579

On the finiteness of quantum K-theory of a homogeneous space

David Anderson·Linda Chen·Hsian-Hua Tseng·Hiroshi Iritani
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Abstract

We show that the product in the quantum K-ring of a generalized flag manifold $G/P$ involves only finitely many powers of the Novikov variables. In contrast to previous approaches to this finiteness question, we exploit the finite difference module structure of quantum K-theory. At the core of the proof is a bound on the asymptotic growth of the $J$-function, which in turn comes from an analysis of the singularities of the zastava spaces studied in geometric representation theory. An appendix by H. Iritani establishes the equivalence between finiteness and a quadratic growth condition on certain shift operators.

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David Anderson, Linda Chen, Hsian-Hua Tseng, Hiroshi Iritani. 2018-04-12. On the finiteness of quantum K-theory of a homogeneous space. https://arxiv.org/abs/1804.04579

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