@article{qpr,
	author = {Gerard Helminck},
	title = { STRICT VERSIONS OF VARIOUS MATRIX HIERARCHIES RELATED TO SLn-LOOPS AND THEIR COMBINATIONS},
	journal = {Quarterly Physics Review},
	volume = {3},
	number = {2},
	year = {2017},
	keywords = {},
	abstract = {Let t be a commutative Lie subalgebra of sln(C) of maximaldimension. 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 ofsolutions.},
	issn = {2572-701X},	url = {https://esmed.org/MRA/qpr/article/view/1408}
}