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Total positivity in twisted product of flag varieties

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arxiv 2211.11168 v2 pith:HEEWTVKI submitted 2022-11-21 math.RT math.AGmath.COmath.GN

Huanchen Bao , Xuhua He This is my paper · ORCID
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We show that the totally nonnegative part of the twisted product of flag varieties of a Kac-Moody group admits a cellular decomposition, and the closure of each cell is a topological manifold with boundary. We also establish explicit parameterizations of each totally positive cell. In the special cases of double flag varieties and braid varieties, we show that the totally nonnegative parts are regular CW complexes homeomorphic to closed balls. Moreover, we prove that the link of any totally nonnegative double Bruhat cell in a reductive group is a regular CW complex homeomorphic to a closed ball, solving an open problem of Fomin and Zelevinsky.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Upper cluster structure on Kac--Moody Richardson varieties

    math.RT 2025-06 conditional novelty 7.0 of 10

    Open Richardson varieties in symmetrizable Kac-Moody flag varieties, including twisted-product cases, are shown to carry upper cluster algebra coordinate rings.

  2. Towards Monoidal Categorifications of Twisted Products of Flag Varieties

    math.RT 2026-02 conditional novelty 6.0 of 10

    The Grothendieck ring of the intersection of two monoidal categories C(β)∩C_v contains the cluster algebra of the twisted product of flag varieties, with cluster monomials given by classes of simple objects.

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