Home > Medical Research Archives > Issue 149 > STRICT VERSIONS OF VARIOUS MATRIX HIERARCHIES RELATED TO SLn-LOOPS AND THEIR COMBINATIONS
Published in the Medical Research Archives
Jul 2017 Issue
STRICT VERSIONS OF VARIOUS MATRIX HIERARCHIES RELATED TO SLn-LOOPS AND THEIR COMBINATIONS
Published on Jul 01, 2017
DOI
Abstract
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.
Author info
Gerard Helminck
Author Area
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