Commuting matrix differential operators and loop algebras
نویسندگان
چکیده
منابع مشابه
On Commuting Matrix Differential Operators
If the differential expressions P and L are polynomials (over C) of another differential expression they will obviously commute. To have a P which does not arise in this way but satisfies [P,L] = 0 is rare. Yet the question of when it happens has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs (P,L). In this paper the question is answered in the...
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The theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs (P,L). Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the differential equations Ly = zy, z ∈ C, are meromorphic. In this paper this relationship is explored ...
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Recently J.A.Anquela, T.Cortés, and H.Petersson [2] proved that for elements x, y in a non-degenerate Jordan algebra J , the relation x ◦ y = 0 implies that the U -operators of x and y commute: UxUy = UyUx. We show that the result may be not true without the assumption on nondegeneracity of J . We give also a more simple proof of the mentioned result in the case of linear Jordan algebras, that ...
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0.1. Our motivation for writing this paper was twofold. On the one hand, we are trying to make sense of the notion of D-module on some infinite-dimensional variety attached to an algebraic group, and on the other hand, we study the structure of a certain interesting representation of the corresponding affine algebra. First, we will explain the representation-theoretic side of the picture. Thus,...
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 2001
ISSN: 0007-4497
DOI: 10.1016/s0007-4497(01)01088-0