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Extensions of differential representations of SL2 and tori

Published online by Cambridge University Press:  16 May 2012

Andrey Minchenko  and
Alexey Ovchinnikov
Andrey Minchenko
Affiliation:
University of Western Ontario, Department of Mathematics, London, ON, N6A 5B7, Canada([email protected])
Alexey Ovchinnikov
Affiliation:
Queens College, Department of Mathematics, 65-30 Kissena Blvd, Flushing, NY 11367, USA([email protected])
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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.

Keywords

differential algebraic groupsdifferential representation theoryrepresentation theory of SL2differential Hopf algebras12H0513N1020G05
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 12 , Issue 1 , January 2013 , pp. 199 - 224
Copyright
Copyright © Cambridge University Press 2013

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