STRICT VERSIONS OF VARIOUS MATRIX HIERARCHIES RELATED TO SLn-LOOPS AND THEIR COMBINATIONS

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Gerard Franciscus Helminck http://orcid.org/0000-0001-7022-5852

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.

Article Details

How to Cite
HELMINCK, Gerard Franciscus. STRICT VERSIONS OF VARIOUS MATRIX HIERARCHIES RELATED TO SLn-LOOPS AND THEIR COMBINATIONS. Quarterly Physics Review, [S.l.], v. 3, n. 2, july 2017. ISSN 2572-701X. Available at: <https://esmed.org/MRA/qpr/article/view/1408>. Date accessed: 21 dec. 2024.
Section
Research Articles

References

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