A restriction theorem for semisimple Lie groups of rank one

Author:
Juan A. Tirao

Journal:
Trans. Amer. Math. Soc. **279** (1983), 651-660

MSC:
Primary 22E46

DOI:
https://doi.org/10.1090/S0002-9947-1983-0709574-9

MathSciNet review:
709574

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Abstract: Let be a Cartan decomposition of a real semisimple Lie algebra and let be the corresponding complexification. Also let be a maximal abelian subspace of and let be the complex subspace of generated by . We assume . Now let be the adjoint group of and let be the analytic subgroup of with Lie algebra . If denotes the ring of all polynomial functions on then clearly is a -module and a fortiori a -module. In this paper, we determine the image of the subring of -invariants in under the restriction map .

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0709574-9

Article copyright:
© Copyright 1983
American Mathematical Society