A generic -invariant in a multiplicity-free -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 on a vector space , we construct a formal power series that is shown to have a nonzero projection to every -isotypic component of . When is multiplicity-free, these "Fourier components" of the function provide all the -invariants in for some spherical subgroup of . Three interesting examples are presented.

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DOI:
https://doi.org/10.1090/S0002-9939-1992-1086348-4

Article copyright:
© Copyright 1992
American Mathematical Society