The monodromy representations of local systems associated with Lauricella's F_D

2016/04/21 by Keiji Matsumoto, Matsumoto, Keiji
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Primary 32S40 #Secondary 33C65

paper · pdf · doi:10.48550/arxiv.1604.06226

openalex publication_date 2016/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give the monodromy representations of local systems of twisted homology groups associated with Lauricella's system F_D(a,b,c) of hypergeometric differential equations under mild conditions on parameters. Our representation is effective even in some cases when the system F_D(a,b,c) is reducible. We characterize invariant subspaces under our monodromy representations by the kernel or image of a natural map from a finite twisted homology group to locally finite one.

Related

• The monodromy representation of Lauricella's hypergeometric function F_C
• Irreducibility of the monodromy representation of Lauricella's F_C
• Relative twisted homology and cohomology groups associated with Lauricella's F_D
• Monodromy representations of hypergeometric systems with respect to fundamental series solutions
• Lauricella's F_C with finite irreducible monodromy group