Algebras of invariant affinors of homogeneous spaces of the real simple Lie groups of the type \(A_l\) with regular isotropy subgroups (Q1603034)

In this paper the author computes the algebra \(\text{End}_{\widetilde{G}}T(M)\) of endomorphisms of the tangent bundle \(T(M)\) in the case of homogeneous spaces \(M=\widetilde{G}/G\) with \(\widetilde{G}\) a real simple Lie group of type \(A_l\) and \(G\) a connected regular semi-simple subgroup of \(\widetilde{G}\). The algebra \(\text{End}_{\widetilde{G}}T(M)\) is an important characteristic of \(M\), and its knowledge is useful when one has to analyse the existence of invariant almost complex, almost quaternion or almost tangent structures.