Education in mathematics and physics at the University of Utrecht.After that, positions at respectively CWI, University of Twente and the University of Amsterdam.
In this paper one considers commutative subalgebras of the Z × Z-matrices generated by a maximal ... more In this paper one considers commutative subalgebras of the Z × Z-matrices generated by a maximal commutative subalgebra of the complex k ×k-matrices and a shift matrix that commutes with them. Key objects are parameter dependent perturbations of these algebras inside the upper triangular Z × Z-matrices such that the perturbed generators satisfy Lax equations with respect to an infinite number of commuting directions. Various appropriate geometric settings are described in which one can actually construct solutions of these hierarchies.
Journal of Physics A-mathematical and General, 2002
In this paper, we introduce the infinite-dimensional flag varieties associated with integrable sy... more In this paper, we introduce the infinite-dimensional flag varieties associated with integrable systems of the KdV- and Toda-type and discuss the structure of these manifolds. As an example we treat the Fubini-Study metric on the projective space associated with a separable complex Hilbert space and conclude by showing that all flag varieties introduced before possess a Kähler structure.
In this paper one considers commutative subalgebras of the Z × Z-matrices generated by a maximal ... more In this paper one considers commutative subalgebras of the Z × Z-matrices generated by a maximal commutative subalgebra of the complex k ×k-matrices and a shift matrix that commutes with them. Key objects are parameter dependent perturbations of these algebras inside the upper triangular Z × Z-matrices such that the perturbed generators satisfy Lax equations with respect to an infinite number of commuting directions. Various appropriate geometric settings are described in which one can actually construct solutions of these hierarchies.
Journal of Physics A-mathematical and General, 2002
In this paper, we introduce the infinite-dimensional flag varieties associated with integrable sy... more In this paper, we introduce the infinite-dimensional flag varieties associated with integrable systems of the KdV- and Toda-type and discuss the structure of these manifolds. As an example we treat the Fubini-Study metric on the projective space associated with a separable complex Hilbert space and conclude by showing that all flag varieties introduced before possess a Kähler structure.
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