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

Zhu, Chen-bo

doi:10.1090/S0002-9939-1992-1086348-4

A generic $H$-invariant in a multiplicity-free $G$-action
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Proc. Amer. Math. Soc. 115 (1992), 629-635 Request permission

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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