Multiplicity one theorems: the Archimedean case | Annals of Mathematics

Abstract Let G be one of the classical Lie groups GLn+1(ℝ), GLn+1(ℂ), U(p,q+1), O(p,q+1), On+1(ℂ), SO(p,q+1), SOn+1(ℂ), and let G′ be respectively the subgroup GLn(ℝ), GLn(ℂ), U(p,q), O(p,q), On(ℂ), SO(p,q), SOn(ℂ), embedded in G in the standard way. We show that every irreducible Casselman-Wallach representation of G′ occurs with multiplicity at most one in every irreducible Casselman-Wallach representation of G. Similar results are proved for the Jacobi groups GLn(ℝ)⋉H2n+1(ℝ), GLn(ℂ)⋉H2n+1(ℂ), U(p,q)⋉H2p+2q+1(ℝ), Sp2n(ℝ)⋉H2n+1(ℝ), Sp2n(ℂ)⋉H2n+1(ℂ), with their respective subgroups GLn(ℝ), GLn(ℂ), U(p,q), Sp2n(ℝ), and Sp2n(ℂ).

KEYWORDS

SHARE & LIKE

数学年刊（Annals of Mathematics）

0 Following 0 Fans 0 Projects 674 Articles

SIMILAR ARTICLES

Abstract For any nondegenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a correspondin

Abstract For a large class of nonlinear Schrödinger equations with nonzero conditions at infinity and for any speed c less than the sound velocity, we

Abstract Let L2,p(ℝ2) be the Sobolev space of real-valued functions on the plane whose Hessian belongs to Lp. For any finite subset E⊂ℝ2 and p>2, let

Abstract We prove that for any group G in a fairly large class of generalized wreath product groups, the associated von Neumann algebra LG completely

Abstract We study the parity of 2-Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve E over an arbitrary number field K. We

Abstract This paper has two main results. Firstly, we complete the parametrisation of all p-blocks of finite quasi-simple groups by finding the so-cal

Abstract We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for ge

Abstract We prove that isoparametric hypersurfaces with (g,m)=(6,2) are homogeneous, which answers Dorfmeister-Neher’s conjecture affirmatively and so

Abstract We prove the periodicity conjecture for pairs of Dynkin diagrams using Fomin-Zelevinsky’s cluster algebras and their (additive) categorificat

Abstract If F(x,y)∈ℤ[x,y] is an irreducible binary form of degree k≥3, then a theorem of Darmon and Granville implies that the generalized superellipt