Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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

Author: Lawrence Corwin
Journal: Trans. Amer. Math. Soc. 264 (1981), 113-120
MSC: Primary 22E30; Secondary 58G15
MathSciNet review: 597870
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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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Article copyright: © Copyright 1981 American Mathematical Society