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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A generic $ H$-invariant in a multiplicity-free $ G$-action

Author: Chen-bo Zhu
Journal: Proc. Amer. Math. Soc. 115 (1992), 629-635
MSC: Primary 20G05; Secondary 15A72
MathSciNet review: 1086348
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Abstract: For a prehomogeneous action of a reductive group $ G$ on a vector space $ V$, we construct a formal power series $ L$ that is shown to have a nonzero projection to every $ G$-isotypic component of $ P(V)$. When $ (G,V)$ is multiplicity-free, these "Fourier components" of the function $ L$ provide all the $ H$-invariants in $ P(V)$ for some spherical subgroup $ H$ of $ G$. Three interesting examples are presented.

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PII: S 0002-9939(1992)1086348-4
Article copyright: © Copyright 1992 American Mathematical Society

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