| Summary: | Let <inline-formula> <math display="inline"> <semantics> <mrow> <mi>G</mi> <mo>/</mo> <mi>H</mi> </mrow> </semantics> </math> </inline-formula> be a homogeneous space of a compact simple classical Lie group <i>G</i>. Assume that the maximal torus <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>H</mi> </msub> </semantics> </math> </inline-formula> of <i>H</i> is conjugate to a torus <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>β</mi> </msub> </semantics> </math> </inline-formula> whose Lie algebra <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="fraktur">t</mi> <mi>β</mi> </msub> </semantics> </math> </inline-formula> is the kernel of the maximal root <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula> of the root system of the complexified Lie algebra <inline-formula> <math display="inline"> <semantics> <msup> <mi mathvariant="fraktur">g</mi> <mi>c</mi> </msup> </semantics> </math> </inline-formula>. We prove that such homogeneous space is formal. As an application, we give a short direct proof of the formality property of compact homogeneous 3-Sasakian spaces of classical type. This is a complement to the work of Fernández, Muñoz, and Sanchez which contains a full analysis of the formality property of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>O</mi> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-bundles over the Wolf spaces and the proof of the formality property of homogeneous 3-Sasakian manifolds as a corollary.
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