Bethe algebra and the algebra of functions on the space of differential operators of order two with polynomial kernel
✍ Scribed by E. Mukhin; V. Tarasov; A. Varchenko
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2008
- Tongue
- English
- Weight
- 359 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1022-1824
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We prove that the scalar and 2 = 2 matrix differential operators which preserve the simplest scalar and vector-valued polynomial modules in two variables have a fundamental Lie algebraic structure. Our approach is based on a general graphical method which does not require the modules to be irreducib
The space of linear differential operators on a smooth manifold M has a natural one-parameter family of Diff(M )-(and Vect(M )-) module structures, defined by their action on the space of tensor densities. It is shown that, in the case of secondorder differential operators, the Vect(M)-module struct