Degenerate principal series representations of SO(p+1, p)
Journal article, 2015
For odd, the Lie group has a family of complementary series representations realized on the space of real skew symmetric matrices, similar to the Stein's complementary series for . We consider their restriction on the subgroup and prove that they are still irreducible and is equivalent to (a unitarization of) the principal series representation of , and also irreducible under a maximal parabolic subgroup of G.
Harmonic analysis on semisimple and nilpotent Lie groups