Unitarizability of Certain Series of Representations

Vogan, David A.

doi:10.2307/2007074

Cited by 208 publications

(150 citation statements)

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“…With the notation as above assume thatX M (λ 1 , λ 2 ) is hermitian. Then so isX(λ 1 , λ 2 ) and we have Proposition 2.1 (D. Vogan,[V2]). Let γ be a p-bottom layer K-type.…”

Section: Necessary Conditions For Unitarity Coming From Bottom Layer mentioning

confidence: 79%

On the unitary dual of 𝑆𝑝𝑖𝑛(2𝑛,ℂ)

Brega

1999

Trans. Amer. Math. Soc.

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Abstract. In this paper we begin a systematic study of the unitarity question for genuine representations of the group Spin(2n, C). The main result is that we find a class of unitary representations (mostly isolated) analogous to the special unipotent representations defined by D. Barbasch and D. Vogan. In particular the full unitary dual of Spin(2n, C) should be obtainable from this set by complementary series.

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“…With the notation as above assume thatX M (λ 1 , λ 2 ) is hermitian. Then so isX(λ 1 , λ 2 ) and we have Proposition 2.1 (D. Vogan,[V2]). Let γ be a p-bottom layer K-type.…”

Section: Necessary Conditions For Unitarity Coming From Bottom Layer mentioning

confidence: 79%

On the unitary dual of 𝑆𝑝𝑖𝑛(2𝑛,ℂ)

Brega

1999

Trans. Amer. Math. Soc.

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“…One finds a proof of the unitarity of the representation A q in [35]. Following [37] and [36], Sect.…”

Section: The Classification Up To Infinitesimal Equivalencementioning

confidence: 99%

Geometric cycles, Albert algebras and related cohomology classes for arithmetic groups

Schwermer¹

2011

Groups Geom. Dyn.

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Abstract.We discuss the construction of totally geodesic cycles in locally symmetric spaces attached to arithmetic subgroups in algebraic groups G of type F 4 which originate with reductive subgroups of the group G. In many cases, it can be shown that these cycles, to be called geometric cycles, yield non-vanishing (co)homology classes. Since the cohomology of an arithmetic group is related to the automorphic spectrum of the group, this geometric construction of non-vanishing classes leads to results concerning the existence of specific automorphic forms.Mathematics Subject Classification (2010). Primary 11F75, 22E40; Secondary 11F70, 57R95.

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“…Then A q is an irreducible Harish-Chandra module which is unitarizable ( [24], [27]). The corresponding unitary representation is denoted by A q ∈ G 0 (⊂ G).…”

Section: Proof Of Theorem 31 We Fix An Arbitrarymentioning

confidence: 99%