The paper classifies all cases where Lie(P)/Lie(H) is a strictly indecomposable spherical L-module for spherical subgroups H regularly embedded in a parabolic P sharing a common Levi subgroup L, and explicitly computes the spherical roots for each such case.
Leahy, A classification of multiplicity free representations, J
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On computing the spherical roots for a class of spherical subgroups
The paper classifies all cases where Lie(P)/Lie(H) is a strictly indecomposable spherical L-module for spherical subgroups H regularly embedded in a parabolic P sharing a common Levi subgroup L, and explicitly computes the spherical roots for each such case.