Differential Equations and Quantum Groups

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pp: 113–155

DOI: 10.4171/020-1/7

Galois theory of parameterized differential equations and linear differential algebraic groups

Phyllis J. Cassidy[1] and Michael F. Singer[2]

(1) Department of Mathematics, The City College of CUNY, Convent Avenue and 138th Street, NY 10031, New York, USA
(2) Department of Mathematics, North Carolina State University, Campus Box 8205, NC 27695-8205, Raleigh, USA

We present a Galois theory of parameterized linear differential equations where the Galois groups are linear differential algebraic groups, that is, groups of matrices whose entries are functions of the parameters and satisfy a set of differential equations with respect to these parameters. We present the basic constructions and results, give examples, discuss how isomonodromic families fit into this theory and show how results from the theory of linear differential algebraic groups may be used to classify systems of second order linear differential equations.

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