Hilbert measures on orbit spaces of coregular $O_m$-modules

Abstract

We construct canonical measures, referred to as Hilbert measures, on orbit spaces of classical coregular representations of the orthogonal groups $O_m$. 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 $O_m$ is equal to $m$.

12 pages