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arXiv · 2411.13063

Hilbert measures on orbit spaces of coregular $\operatorname{O}_m$-modules

Hans-Christian Herbig·Christopher W. Seaton·Lillian Whitesell
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Abstract

We construct canonical measures, referred to as Hilbert measures, on orbit spaces of classical coregular representations of the orthogonal groups $\operatorname{O}_m$. We observe that the measures have singularities along non-principal strata of the orbit space if and only if the number of copies of the defining representation of $\operatorname{O}_m$ is equal to $m$.

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Hans-Christian Herbig, Christopher W. Seaton, Lillian Whitesell. 2024-11-20. Hilbert measures on orbit spaces of coregular $\operatorname{O}_m$-modules. https://doi.org/10.1016/j.geomphys.2025.105473

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