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

H. Fujiwara, G. Lion, B. Magneron

• 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.