A Flagvariety Relating Matrix Hierarchies and Toda-Type Hierarchies


Helminck, Gerardus F. (2006) A Flagvariety Relating Matrix Hierarchies and Toda-Type Hierarchies. Acta Applicandae Mathematicae, 90 (1-2). pp. 121-142. ISSN 0167-8019

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Abstract:Commutative subalgebras of the complex -matrices are known to generate both matrix and Toda-type hierarchies. In this paper a certain class of infinite chains of closed subspaces of a separable Hilbert space will be introduced. To each such a flag one associates a sequence of solutions of the matrix hierarchy related to this subalgebra. They compose to a solution of the lower triangular Toda hierarchy corresponding to the transposed algebra. Both solutions can be expressed in determinants of suitable Fredholm operators, the so-called τ-functions. These last functions also have a geometric interpretation in terms of line bundles over the flagvariety. They measure the failure of equivariance w.r.t. to the commuting flows of certain global sections.
Item Type:Article
Copyright:© 2006 Springer
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Link to this item:http://purl.utwente.nl/publications/69567
Official URL:https://doi.org/10.1007/s10440-006-9033-6
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