Multiplizit�ten ?unendlich-ferner? Spitzen

LetX be the quotient of a bounded symmetric domainD by an arithmetically defined subgroup Γ of all analytic automorphisms ofD and letX * be theSatake-compactification ofX. In the present note, the multiplicities of the local rings of the zero-dimensional boundary components ofX * will be computed in a completely elementary manner using reduction-theory in selfadjoint homogeneous cones.