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Invariant differential equations on certain semisimple Lie groups


Author: F. Rouvière
Journal: Trans. Amer. Math. Soc. 243 (1978), 97-114
MSC: Primary 22E30; Secondary 58G35
DOI: https://doi.org/10.1090/S0002-9947-1978-0502896-4
MathSciNet review: 502896
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Abstract: If G is a semisimple Lie group with one conjugacy class of Cartan subalgebras (e.g. a complex semisimple Lie group), a bi-invariant differential equation on G can be reduced by means of the Radon transform to one on the subgroup MA. In particular, all polynomials of the Casimir operator have a central fundamental solution, and are solvable in $ {C^\infty }(G)$; but, for G complex, the ``imaginary'' Casimir operator is not.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1978-0502896-4
Keywords: Semisimple Lie groups, bi-invariant differential operators, Radon transform, Casimir operator
Article copyright: © Copyright 1978 American Mathematical Society

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