TY - JOUR AU - Helminck, Gerard Franciscus PY - 2017/07/01 TI - STRICT VERSIONS OF VARIOUS MATRIX HIERARCHIES RELATED TO SLn-LOOPS AND THEIR COMBINATIONS JF - Quarterly Physics Review; Vol 3 No 2 (2017): Vol. 3 Issue 2, July 2017 KW - N2 - Let t be a commutative Lie subalgebra of sln(C) of maximal dimension. We consider in this paper three spaces of t-loops that each get deformed in a different way. We require that the deformed generators of each of them evolve w.r.t. the commuting flows they generate according to a certain, different set of Lax equations. This leads to three integrable hierarchies: the (sln(C), t)-hierarchy, its strict version and the combined (sln(C), t)-hierarchy. For n = 2 and t the diagonal matrices, the (sl2(C), t)- hierarchy is the AKNS-hierarchy. We treat their interrelations and show that all three have a zero curvature form. Furthermore, we discuss their linearization and we conclude by giving the construction of a large class of solutions. UR - https://esmed.org/MRA/qpr/article/view/1408