Correction: The geometry of compact homogeneous spaces with two isotropy summands

We give a complete list of all homogeneous spaces M=G/H where G is a simple compact Lie group, H a connected, closed subgroup, and G/H is simply connected, for which the isotropy representation of H on TₚM decomposes into exactly two irreducible summands. For each homogeneous space, we determine whether it admits a G-invariant Einstein metric. When there is an intermediate subgroup H< K < G, we classify all the G-invariant Einstein metrics. This is an extension of the classification of isotropy irreducible spaces, given independently by Manturov (Dokl Akad Nauk SSSR 141: 792–795, 1961; Dokl Akad Nauk SSSR 141: 1034–1037, 1961; Tensor Semin Vector Anal 13: 68–145, 1966) and Wolf (Acta Math 120: 59–148, 1968; Acta Math 152: 141–142, 1984).