TY - JOUR
AU - Singer, Michael F.
AB - 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 SL2 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.
TI - Reductive Linear Differential Algebraic Groups and the Galois Groups of Parameterized Linear Differential Equations
JF - International Mathematics Research Notices
DO - 10.1093/imrn/rnt344
DA - 2015-01-10
UR - https://www.deepdyve.com/lp/oxford-university-press/reductive-linear-differential-algebraic-groups-and-the-galois-groups-7YU1AWm4cV
SP - 1733
EP - 1793
VL - 2015
IS - 7
DP - DeepDyve
ER -