Invariant Differential Operators on Certain Nilpotent Homogeneous Spaces |
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Authors: | A Baklouti J Ludwig |
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Institution: | (1) Faculté des Sciences de Sfax, Tunisia, TN;(2) Université de Metz, France, FR |
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Abstract: | Let be a nilpotent connected and simply connected Lie group, and an analytic subgroup of G. Let , be a unitary character of H and let . Suppose that the multiplicities of all the irreducible components of τ are finite. Corwin and Greenleaf conjectured that
the algebra of the differential operators on the Schwartz-space of τ which commute with τ is isomorphic to the algebra of H-invariant polynomials on the affine space . We prove in this paper this conjecture under the condition that there exists a subalgebra which polarizes all generic elements
in . We prove also that if is an ideal of , then the finite multiplicities of τ is equivalent to the fact that the algebra is commutative.
(Received 15 November 2000) |
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Keywords: | 2000 Mathematics Subject Classification: 22 E 27 |
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