A representation-theoretic criterion for local solvability of left invariant differential operators on nilpotent Lie groups

Corwin, Lawrence

doi:10.1090/S0002-9947-1981-0597870-6

A representation-theoretic criterion for local solvability of left invariant differential operators on nilpotent Lie groups
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Trans. Amer. Math. Soc. 264 (1981), 113-120 Request permission

Abstract:

Let $L$ be a left invariant differential operator on the nilpotent Lie group $N$. It is shown that if $\pi (L)$ is invertible for all irreducible representations $\pi$ in general position (and if the inverses satisfy some mild technical conditions), then $L$ is locally solvable. This result generalizes a theorem of ${\text {L}}$. Rothschild.

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Linear partial differential operators