Quantum Frobenius splittings and cluster structures

2023/05/20 by Jinfeng Song, Song, Jinfeng
Mathematics · #13F60 #17B37 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2305.12110

openalex publication_date 2023/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the duals of the quantum Frobenius morphisms and their splittings by Lusztig are compatible with quantum cluster monomials. After specialisation, we deduce that the canonical Frobenius splittings on flag varieties are compatible with cluster algebra structures on Schubert cells.

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