Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case)

Global Mixed Periods and Local Klyachko Models for the General Linear Group

“…This map is described explicitly in §3 in terms of Tadic's classification of the unitary dual of G(F ) obtained in [Tad86]. Our proof is local.…”

“…The index κ(π) is expressed in terms of the classification of the unitary dual of G obtained by Tadic in [Tad86]. Our proof is based on the properties of derivatives for representations of G introduced by Gelfand-Kazhdan in [GK75].…”

Annihilator varieties, adduced representations, Whittaker functionals, and rank for unitary representations of GL(n)

“…We can prove the "moreover" part through an analog of Corollary 4.2.2: there is a Tadic classification of the unitary representations as products of certain building blocks (see [Tad86]), from which we see that rank(π) = k < n/2 if and only if π = χ × τ , for some character χ of G n−k and some τ ∈ M(G k ). Since the same holds for Howe rank (by [Sca90, Part II, Corollary 3.2]), the "moreover" part follows.…”

Characters of Speh representations and Lewis Caroll identity

“…The Speh representations u(δ(ρ, l), n), ρ unitary, are the building blocks in the classification of the unitary dual of the groups GL(m, A) (see [13], [14], and Section 4).…”

“…The unitary dual of G m was described in [14] ( [13] in the case A = F ), and the missing part of the proof (conjectures U 0 and U 1 in [14]) were obtained respectively in [11] and [2]. Speh representations are building blocks for the unitary dual of G m , in the sense that an irreducible unitary representation of G m is always fully parabolically induced from a tensor product of Speh representations or complementary series starting from a tensor product of two copies of the same Speh representation (see Section 4).…”