A commutativity criterion for certain algebras of invariant differential operators on nilpotent homogeneous spaces

• Autores: H. Fujiwara, G. Lion, B. Magneron
• Localización: Mathematische Annalen, ISSN 0025-5831, Vol. 326, Nº 3, 2003, pág. 513
• Idioma: inglés
• DOI: 10.1007/s00208-003-0464-3
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• Resumen

  • Let G be a connected, simply connected real nilpotent Lie group with Lie algebra ?, H a connected closed subgroup of G with Lie algebra ? and f a linear form on ? satisfying f([?, ?]) = {0}⋅ Let χ f be the unitary character of H with differential −1−−−√f at the origin. Let τ f be the unitary representation of G induced from the character χ f of H. We consider the algebra ?(?, ?, f) of differential operators invariant under the action of G on the bundle with basis G/H associated to these data. We show that ?(?, ?, f) is commutative if and only if τ f is of finite multiplicities. This proves a conjecture of Corwin-Greenleaf and Duflo.