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

David Anderson Ohio State University Linda Chen Swarthmore College Hsian-Hua Tseng Ohio State University

Combinatorics Representation Theory mathscidoc:1907.01005

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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@inproceedings{davidon,
  title={On the finiteness of quantum K-theory of a homogeneous space},
  author={David Anderson, Linda Chen, and Hsian-Hua Tseng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190702224334788937395},
}
David Anderson, Linda Chen, and Hsian-Hua Tseng. On the finiteness of quantum K-theory of a homogeneous space. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190702224334788937395.
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