Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations

Andrey Minchenko; Alexey Ovchinnikov; Michael F. Singer

doi:10.1093/imrn/rnt344

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arXiv · 1304.2693

Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations

Andrey Minchenko·Alexey Ovchinnikov·Michael F. Singer

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Abstract

We develop the representation theory for reductive linear differential algebraic groups (LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives in differential representations of reductive LDAGs, extending existing results, which were obtained for SL(2) in the case of just one derivation. As an application of the above bound, we develop an algorithm that tests whether the parameterized differential Galois group of a system of linear differential equations is reductive and, if it is, calculates it.

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Andrey Minchenko, Alexey Ovchinnikov, Michael F. Singer. 2013-04-09. Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations. https://doi.org/10.1093/imrn%2Frnt344

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