Generating Rational Loop Groups with Noncompact Reality Conditions

Autores: Oliver Goertsches
Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 113, Nº 2, 2013, págs. 187-205
Idioma: inglés
DOI: 10.7146/math.scand.a-15569
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Resumen
- We find generators for the full rational loop group of ${\rm GL}(n,\mathsf{C})$ as well as for the subgroup consisting of loops that satisfy the reality condition with respect to the noncompact real form ${\rm GL}(n,\mathsf{R})$. We calculate the dressing action of some of those generators on the positive loop group, and apply this to the ZS-AKNS flows and the $n$-dimensional system associated to ${\rm GL}(n,\mathsf{R})/{\rm O}(n)$.