Erratum: ''Parallelizability of homogeneous spaces. II'' (Q1088209)

In the list of stably parallelizable quotients [ibid. 274, 157-176 (1986; Zbl 0572.57014), Theorem 2], case (vi) is wrongly stated. It should read: (vi) \(Sp(n)/(SU(2)\times...\times SU(2))=Z_{n,k}\), where k denotes the number of factors SU(2), with 2k\(\leq n\). As a consequence, Theorem 1 and the ensuing discussion require the additional hypothesis that G is not isomorphic to Sp(n), \(n\geq 4\). In the general case, we have instead: Theorem \(1^*\). Let G be a simple 1-connected compact Lie group and H a closed connected subgroup. Denote by I the ideal of RO(H) which is generated by the elements \[ (\psi | H-\dim \psi)\text{ where } \psi \in RO(G),\quad and\quad \phi \cdot (\lambda | H- \dim_{{\mathbb{C}}}\lambda)\text{ where } \phi \in RSp(H),\quad \lambda \in RSp(G)\quad. \] Then G/H is stably parallelizable if and only if \((Ad_ H-\dim H)\in I\).