An analytic framework for the two-dimensional infinite Toda hierarchy associated with a commutative algebra

G. F. Helminck^a, S. V. Polenkova<sup>b

a</sup> University of Amsterdam
^b University of Twente

Abstract: Starting with the group of operators on a separable Hilbert space that differ from the identity by a trace-class operator, we construct a solution of the two-dimensional infinite Toda hierarchy associated with a maximal commutative subalgebra in complex $k{\times}k$ matrices.

Keywords: two-dimensional infinite Toda hierarchy, Lax equation, linearization, commuting flows, Banach Lie group, big cell.

DOI: 10.4213/tmf6202

 English version: Theoretical and Mathematical Physics, 2008, 155:1, 659–672

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