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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Minchenko, Andrei and Ovchinnikov, Alexey 2018. Calculating Galois groups of third-order linear differential equations with parameters. Communications in Contemporary Mathematics, Vol. 20, Issue. 04, p. 1750038.
    Hardouin, Charlotte Minchenko, Andrei and Ovchinnikov, Alexey 2017. Calculating differential Galois groups of parametrized differential equations, with applications to hypertranscendence. Mathematische Annalen, Vol. 368, Issue. 1-2, p. 587.
    Minchenko, Andrey Ovchinnikov, Alexey and Singer, Michael F. 2015. Reductive Linear Differential Algebraic Groups and the Galois Groups of Parameterized Linear Differential Equations. International Mathematics Research Notices, Vol. 2015, Issue. 7, p. 1733.
    Gorchinskiy, Sergey and Ovchinnikov, Alexey 2014. Isomonodromic differential equations and differential categories. Journal de Mathématiques Pures et Appliquées, Vol. 102, Issue. 1, p. 48.
    Gillet, Henri Gorchinskiy, Sergey and Ovchinnikov, Alexey 2013. Parameterized Picard–Vessiot extensions and Atiyah extensions. Advances in Mathematics, Vol. 238, Issue. , p. 322.
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Extensions of differential representations of SL2 and tori

  • Andrey Minchenko (a1) and Alexey Ovchinnikov (a2)
Abstract

Linear differential algebraic groups (LDAGs) measure differential algebraic dependencies among solutions of linear differential and difference equations with parameters, for which LDAGs are Galois groups. Differential representation theory is a key to developing algorithms computing these groups. In the rational representation theory of algebraic groups, one starts with and tori to develop the rest of the theory. In this paper, we give an explicit description of differential representations of tori and differential extensions of irreducible representation of . In these extensions, the two irreducible representations can be non-isomorphic. This is in contrast to differential representations of tori, which turn out to be direct sums of isotypic representations.

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