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Article: Study results from D.I. Panyushev and colleagues in the area of mathematics published.
- Article from:
- Journal of Mathematics
- Article date:
- February 17, 2009
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According to recent research from Russia, "Let G be a semisimple algebraic group with Lie algebra g. In 1979, J. Dixmier proved that any vector field annihilating all G-invariant polynomials on g lies in the k[g]-module generated by the 'adjoint vector fields', that is, vector fields zeta of the form zeta(y)(x) = [x, y], x, y epsilon g. A substantial generalisation of Dixmier's theorem was found by Levasseur and Stafford."
"They explicitly described the centraliser of k[g](G) in the algebra of differential operators on g. On the level of vector fields, their result reduces to Dixmier's theorem," wrote D.I. Panyushev and colleagues.
The researchers ...