Quantum $K$-theory of $G/P$ and $K$-homology of affine Grassmannian

Chi Hong Chow; Naichung Conan Leung

Quantum $K$-theory of $G/P$ and $K$-homology of affine Grassmannian

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arxiv 2201.12951 v1 pith:V3JUGEF7 submitted 2022-01-31 math.AG math.KT

Chi Hong Chow , Naichung Conan Leung This is my paper · ORCID

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keywords firstproofaffineanalogueauthorcaseconjectureextension

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abstract

This paper is the $K$-theoretic analogue of a recent new proof, given by the first named author, of Peterson-Lam-Shimozono's theorem via Savelyev's generalization of Seidel representations. The outcome is a new proof of Lam-Li-Mihalcea-Shimozono's conjecture, including its extension to the parabolic case, which was first verified by Kato.

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Towards small quantum Chern character
math.AG 2025-07 conditional novelty 7.0 of 10

A quantum Chern character ring homomorphism is constructed for projective spaces and incidence varieties, and a new presentation of small quantum K-theory of Milnor hypersurfaces is proved.

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