P-invariant distributions on GL(N) and the classification of unitary representations of GL(N) (Non-archimedean case)

On a new functional equation for local integrals

“…Then π = π 1 ⊗π 1 where π 1 is an irreducible unitarizable representations of GL n (F ). It is known that A 1 isG-invariant [Ber84,Bar03].…”

Equidistribution in supersingular Hecke orbits

“…We claim that Arthur's condition is true if we take v := p and k := χ G(Qp) c f . The group G(Q p ) is a product of general linear groups, therefore parabolic induction of an unitary representation from a proper Levi subgroup is irreducible [4]. The representation π p is a full induction of the form Ind Combining the previous considerations (Eq.…”

Symplectic periods of the continuous spectrum of \mathrm{GL}(2n)

“…As a representation of G(A) induced from a unitary representation, I(π) is known to be irreducible [2,13]. For s ∈ a * L,C we study the Eisenstein series…”