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

PDF
Restricted to UT campus only: Request a copy
252Kb

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
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Link to this item:	http://purl.utwente.nl/publications/69567
Official URL:	http://dx.doi.org/10.1007/s10440-006-9033-6
Export this item as:	BibTeX EndNote HTML Citation Reference Manager

Show download statistics for this publication

Repository Staff Only: item control page