Let H be a closed connected subgroup of a compact connected Lie group G. If rank(G) = rank(H), it is well known that the rational cohomology of G/H concentrates in even degrees hence the isotropy action of H on G/H is equivariantly formal. In this talk, we will consider the case where rank(G) - rank(H) = 1 and give a characterization of equivariantly formal isotropy action in this case.

with relations. This settles a conjecture by Stroppel (ICM 2010) on the bigraded Hochschild cohomology groups of extended Khovanov arc algebras. This is based on a joint work with Severin Barmeier.