
Journal of Lie Theory 29 (2019), No. 3, 755786 Copyright Heldermann Verlag 2019 Isometric Actions of Quaternionic Symplectic Groups Manuel SedanoMendoza Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Morelia  Michoacán, Mexico msedano@matmor.unam.mx [Abstractpdf] Denote by $Sp(k,l)$ the quaternionic symplectic group of signature $(k,l)$. We study the deformation rigidity of the embedding $Sp(k,l) \times Sp(1) \hookrightarrow H$, where $H$ is either $Sp(k+1,l)$ or $Sp(k,l+1)$, this is done by studying a natural nonassociative algebra $\mathfrak{m}$ coming from the affine structure of $Sp(1) \backslash H$. We compute the automorphism group of $\mathfrak{m}$ and as a consecuence of this, we are able to compute the isometry group of $Sp(1) \backslash H$ at least up to connected components. Using these results, we obtain a uniqueness result on the structure of $Sp(1) \backslash H$ together with an isometric left $Sp(k,l)$action and classify its finite volume quotients up to finite coverings. Finally, we classify arbitrary isometric actions of $Sp(k,l)$ into connected, complete, analytic, pseudoRiemannian manifolds of dimension bounded by $\textrm{dim}(Sp(1) \backslash H)$ that admit a dense orbit. Keywords: PseudoRiemannian manifolds, rigidity results, noncompact quaternionic symplectic groups. MSC: 22F30, 17B40, 53C24 [ Fulltextpdf (231 KB)] for subscribers only. 