Modular invariants of finite gluing groups

2019/10/07 by Yin Chen, Chen, Yin, R. James Shank +3 · 1 citation
Mathematics · #13A50 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1910.02659

openalex publication_date 2019/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the gluing construction introduced by Jia Huang to explore the rings of invariants for a range of modular representations. We construct generating sets for the rings of invariants of the maximal parabolic subgroups of a finite symplectic group and their common Sylow p-subgroup. We also investigate the invariants of singular finite classical groups. We introduce parabolic gluing and use this construction to compute the invariant field of fractions for a range of representations. We use thin gluing to construct faithful representations of semidirect products and to determine the minimum dimension of a faithful representation of the semidirect product of a cyclic p-group acting on an elementary abelian p-group.

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• Representations of finite subgroups of Cremona groups

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