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Tyurin parameters of commuting pairs and infinite dimensional Grassmann manifold | | Kanehisa Takasaki
; | | Date: |
2 May 2005 | | Subject: | Exactly Solvable and Integrable Systems; Algebraic Geometry; Mathematical Physics | nlin.SI hep-th math-ph math.AG math.MP | | Abstract: | Commuting pairs of ordinary differential operators are classified by a set of algebro-geometric data called ``algebraic spectral data’’. These data consist of an algebraic curve (``spectral curve’’) $Gamma$ with a marked point $gamma_infty$, a holomorphic vector bundle $E$ on $Gamma$ and some additional data related to the local structure of $Gamma$ and $E$ in a neighborhood of $gamma_infty$. If the rank $r$ of $E$ is greater than 1, one can use the so called ``Tyurin parameters’’ in place of $E$ itself. The Tyurin parameters specify the pole structure of a basis of joint eigenfunctions of the commuting pair. These data can be translated to the language of an infinite dimensional Grassmann manifold. This leads to a dynamical system of the standard exponential flows on the Grassmann manifold, in which the role of Tyurin parameters and some other parameters is made clear. | | Source: | arXiv, nlin.SI/0505005 | | Services: | Forum | Review | PDF | Favorites | |
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