  Studying the isotropy orbits of compact symmetric spaces Reiswich introduced
a family of explicit polynomials in one variable in order to describe the
unique minimal isotropy orbit of compact symmetric spaces with Dynkin diagram
of type $D_m$. Based on this geometric interpretation he conjectured that these
polynomials all have pairwise different real roots in the interval $[\,0,1\,]$.
In this article the polynomials constructed by Reiswich will be identified as
special cases of Jacobi polynomials thus proving the conjecture about minimal
isotropy orbits of compact symmetric spaces with Dynkin diagram of type $D_m$.
