Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



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
MathSciNet review: 502896
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E30, 58G35

Retrieve articles in all journals with MSC: 22E30, 58G35

Additional Information

Keywords: Semisimple Lie groups, bi-invariant differential operators, Radon transform, Casimir operator
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society