On the Classification of Schubert Varieties in Partial Flag Varieties

2024/12/03 by Y. Chen, Chen, Yanjun
Computer Science · Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2412.02150

openalex publication_date 2024/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the classification of isomorphism classes of Schubert varieties in complete flag varieties G/B to a class of partial flag varieties G/P. In particular, we classify all Schubert varieties in G/P where P is a minimal parabolic subgroup and all Schubert surfaces. We also obtain several pairs of isomorphisms of Schubert varieties from folding the root system. This allows us to find an upper bound of the cardinality of isomorphism classes of Schubert three-folds.

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