A proof of Kirillov's conjecture

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Multiplicity one theorems: the Archimedean case (2009, background): “Ln(K). We remark that under the additional assumption that the generalized function is an eigenvector of the algebra of bi-invariant diﬀerential operators on GLn(K), Corollary C is the main result of [Ba03] (Theorem 1.4). As observed by Kirillov, this implies the validity of his famous conjecture on”
Multiplicity one theorem for (GL_n+1 (R), GL_n(R)) (2008, background): “roup consisting of all matrices whose last row is (0,...,0,1). Let GLn act on itself by conjugation. Then every Pn(F) - invariant distribution on GLn(F) is GLn(F) - invariant. This has been proven in [Bar] for eigendistributions with respect to the center of UC(gln). In [Bar] it is also shown that t”
Unitary dual of GL(n) at archimedean places and global Jacquet–Langlands correspondence (2009, background): “Vogan’s classification and U(0) in the archimedean case As we have already said, hypothesis U(0) has been established in the case where A= R or C by work of M. Baruch that filled the serious technical gap remaining in Kirillov’s treatment of Bernstein approach [Kir62].”