Browsing by Author "Xu, Weihong"

Now showing 1 - 3 of 3
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    The isomorphism problem for Grassmannian Schubert varieties
    Tarigradschi, Mihail; Xu, Weihong (Academic Press – Elsevier, 2023-11-01)
    We prove that Schubert varieties in potentially different Grassmannians are isomorphic as varieties if and only if their corresponding Young diagrams are identical up to a transposition. We also discuss a generalization of this result to Grassmannian Richardson varieties. In particular, we prove that Richardson varieties in potentially different Grassmannians are isomorphic as varieties if their corresponding skew diagrams are semi-isomorphic as posets, and we conjecture the converse. Here, two posets are said to be semi-isomorphic if there is a bijection between their sets of connected components such that the corresponding components are either isomorphic or opposite.
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    Quantum K theory of partial flag manifolds
    Mihalcea, Constantin; Sharpe, Eric; Gu, Wei; Zhang, Hao; Xu, Weihong; Zou, Hao (Elsevier, 2024-04)
    In this paper we use three-dimensional gauged linear sigma models to make physical predictions for Whitney-type presentations of equivariant quantum K theory rings of partial flag manifolds, as quantum products of universal subbundles and various ratios, extending previous work for Grassmannians. Physically, these arise as OPEs of Wilson lines for certain Chern-Simons levels. We also include a simplified method for computing Chern-Simons levels pertinent to standard quantum K theory.
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    Quantum K Whitney relations for partial flag varieties
    Gu, Wei; Mihalcea, Leonardo C.; Sharpe, Eric; Xu, Weihong; Zhang, Hao; Zou, Hao (2023-10-05)
    In a recent paper, we stated conjectural presentations for the equivariant quantum K ring of partial flag varieties, motivated by physics considerations. In this companion paper, we analyze these presentations mathematically. We prove that if the conjectured relations hold, then they must form a complete set of relations. Our main result is a proof of the conjectured presentation in the case of the incidence varieties. We also show that if a quantum K divisor axiom holds (as conjectured by Buch and Mihalcea), then the conjectured presentation also holds for the complete flag variety.