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Let   G   be a simply connected semisimple algebraic group with Lie algebra   g  , letG  0   ⊂  G    be the symmetric subgroup defined by an algebraic involution   σ   and letg  1   ⊂  g    be the isotropy representation of    G  0   . Given an abelian subalgebra   a   of   g   contained in    g  1    and stable under the action of some Borel subgroupB  0   ⊂   G  0    , we classify the    B  0   ‐orbits in   a   and characterize the sphericity ofG  0   a   . Our main tool is the combinatorics of   σ  ‐minuscule elements in the affine Weyl group of   g   and that of strongly orthogonal roots in Hermitian symmetric spaces.

Spherical nilpotent orbits and abelian subalgebras in isotropy representations