# Weakly irreducible subgroups of $\mbox {Sp}(1,n+1)$

## Natalia I. Bezvitnaya

Address: Department of Algebra and Geometry, Masaryk University Kotlářská 2, 611 37 Brno, Czech Republic

E-mail: bezvitnaya@math.muni.cz

Abstract: Connected weakly irreducible not irreducible subgroups of $\mbox {Sp}(1,n+1)\subset \mbox {SO}(4,4n+4)$ that satisfy a certain additional condition are classified. This will be used to classify connected holonomy groups of pseudo-hyper-Kählerian manifolds of index 4.

AMSclassification: primary 53C29; secondary 53C50.

Keywords: pseudo-hyper-Kählerian manifold of index 4, weakly irreducible holonomy group.