On The Finiteness Of Quantum K-Theory Of A Homogeneous Space

Authors

D. Anderson
Linda Chen, Swarthmore CollegeFollow
H.-H. Tseng

Document Type

Article

Publication Date

1-1-2022

Published In

International Mathematics Research Notices

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.

Comments

This work is a preprint that is freely available courtesy of Oxford University Press.

Recommended Citation

D. Anderson, Linda Chen, and H.-H. Tseng. (2022). "On The Finiteness Of Quantum K-Theory Of A Homogeneous Space". International Mathematics Research Notices. Volume 2022, Issue 2. 1313-1349. DOI: 10.1093/imrn/rnaa108
https://works.swarthmore.edu/fac-math-stat/271