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Extensions of differential representations of SL2 and tori

Published online by Cambridge University Press:  16 May 2012

Andrey Minchenko
Affiliation:
University of Western Ontario, Department of Mathematics, London, ON, N6A 5B7, Canada(aminchen@uwo.ca)
Alexey Ovchinnikov
Affiliation:
Queens College, Department of Mathematics, 65-30 Kissena Blvd, Flushing, NY 11367, USA(aovchinnikov@qc.cuny.edu)

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.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2013

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