Let G = GLn (K) where K is either R or C and let P = Pn (K) be the subgroup of matrices in GLn (K) consisting of matrices whose last row is (0, 0, . . . , 0, 1). Let π be an irreducible unitary representation of G. Gelfand and Neumark [Gel-Neu] proved that if K = C and π is in the Gelfand-Neumark series of irreducible unitary representations of G then the restriction of π to P remains irreducible. Kirillov [Kir] conjectured that this should be true for all irreducible unitary representations π of GLn.
