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Invariants of classCk for finite coxeter groups and their representations in terms of anisotropic spaces

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Abstract

This article is devoted to the study of representations of Ck {\(C^k \left( {\mathbb{R}^n } \right)\)} functions f invariant with respect to finite Coxeter groups W in the form f=F op, where p is a base in the algebra of W-invariant polynomials. We examine the lowering of smoothness of F as compared with f and conclude that this lowering has an anisotropic nature and that, more precisely, at each point Po it is described by a vector {\(\bar \mu \left( {po} \right) \in \mathbb{R}^n \)}. We examine the cases W=An, Bn, Dn, {\(\mathfrak{D}_m \)}; in each case the greatest component {\(\mu _j \)} of {\(\bar \mu \)} is equal to the Coxeter number of the stabilizer Wyo of the point yo, where po=p(yo). Bibliography: 22 titles.

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  1. A. O. Gokhman
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 46–70.

Translated by S. Yu. Pilyugin.

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Gokhman, A.O. Invariants of classCk for finite coxeter groups and their representations in terms of anisotropic spaces. J Math Sci 101, 3073–3087 (2000). https://doi.org/10.1007/BF02673732

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  • DOI: https://doi.org/10.1007/BF02673732

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