Canonical representations and overgroups for hyperboloids (Q883644)

Let \(G\) be the group \(\text{SO}_{0}(p,q)\), i.e., the identity component of the linear transformations of \(\mathbb{R}^n\), \(n=p+q\), preserving the bilinear form: \[ [x,y]=-x_{1}y_{1}-\dots -x_{p}y_{p}+x_{p+1}y_{p+1}+\dots +x_{n}y_{n}. \] In the paper under review the author studies the representations of \(G\) associated with the hyperboloid \(G/H\), where \(H= \text{SO}_{0}(p,q-1)\).