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On two notions of total positivity for generalized partial flag varieties of classical Lie types

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arxiv 2410.11804 v2 pith:H4MWRJDU submitted 2024-10-15 math.CO math.AGmath.RT

classification math.COmath.AGmath.RT
keywords positivitytotalflagpartialtypevarietiescoincideslusztig
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For Grassmannians, Lusztig's notion of total positivity coincides with positivity of the Plucker coordinates. This coincidence underpins the rich interaction between matroid theory, tropical geometry, and the theory of total positivity. Bloch and Karp furthermore characterized the (type A) partial flag varieties for which the two notions of positivity similarly coincide. We characterize the symplectic (type C) and odd-orthogonal (type B) partial flag varieties for which Lusztig's total positivity coincides with Plucker positivity.

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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. Totally positive skew-symmetric matrices

    math.CO 2024-12 conditional novelty 7.0 of 10

    An n×n skew-symmetric matrix is totally positive exactly when its n(n−1)/2 selected signed minors are positive, and its Pfaffians then follow one universal sign rule.

  2. The positive orthogonal Grassmannian

    math.CO 2024-12 conditional novelty 7.0 of 10

    For the positive orthogonal Grassmannian, the authors describe boundaries in the simplest case, prove a duality between two special families, and show the standard cell decomposition fails when n>2k+1.

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