A Root Parametrized Differential Equation for the Special Linear Group

2014/05/05 by Matthias Seiß, Seiß, Matthias
Mathematics · #12H05 #13N99 #Algebraic and Geometric Analysis #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1405.0925

openalex publication_date 2014/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C ⟨ \boldsymbolt ⟩ be the differential field generated by l differential indeterminates \boldsymbolt=(t₁, …, t_l) over an algebraically closed field C of characteristic zero. In this article we present an explicit linear parameter differential equation over C ⟨ \boldsymbolt ⟩ with differential Galois group SL_l+1(C) and show that it is a generic equation in the following sense: If F is an algebraically closed differential field with constants C and E/F is a Picard-Vessiot extension with differential Galois group H(C) ⊆ SL_l+1(C), then a specialization of our equation defines a Picard-Vessiot extension differentially isomorphic to E/F.

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