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Trapa, Peter E.

doi:10.1023/a:1013115223377

Cited by 27 publications

(1 citation statement)

References 28 publications

(13 reference statements)

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“…In this good parity setting, we will state a counting result on Unip Ǒ(G). The elements in Unip Ǒ(G) can be constructed by cohomological induction explicitly and they are irreducible and unitary due to [Mat96,Tra01], see also [Tra04, Section 2] and [MR19, Section 4]. We refer the reader to [BMSZ21] for the construction of all elements of Unip Ǒ(G) by the method of theta lifting.…”

Section: The Case When ⋆mentioning

confidence: 99%

Special unipotent representations of real classical groups: counting and reduction to good parity

Barbasch¹,

Ma²,

Sun³

et al. 2022

Preprint

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Let G be a real reductive group in Harish-Chandra's class. We derive some consequences of theory of coherent continuation representations to the counting of irreducible representations of G with a given infinitesimal character and a given bound in the complex associated variety. When G is a real classical group (including the real metaplectic group), we investigate the set of special unipotent representations of G attached to Ǒ, in the sense of Barbasch and Vogan. Here Ǒ is a nilpotent adjoint orbit in the Langlands dual of G (or the metaplectic dual of G when G is a real metaplectic group). We give a precise count for the number of special unipotent representations of G attached to Ǒ. We also reduce the problem of constructing special unipotent representations attached to Ǒ to the case when Ǒ has good parity. The paper is the first in a series of two papers on the classification of special unipotent representations of real classical groups.

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Section: The Case When ⋆mentioning

confidence: 99%

Special unipotent representations of real classical groups: counting and reduction to good parity

Barbasch¹,

Ma²,

Sun³

et al. 2022

Preprint

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One-Dimensional Representations of U (p,q) and the Howe Correspondence

Paul

Trapa

2002

Journal of Functional Analysis

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We explicitly determine the theta lifts of all one-dimensional representations of Uðp; qÞ in terms of Langlands parameters, and determine exactly which lifts are unitary. Moreover, we show that such a lift is unitary if and only if it is a weakly fair derived functor module of the form A q ðlÞ: Finally, we show that the correspondence of unitary representations behaves well with respect to associated cycles. # 2002 Elsevier Science (USA)

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Restrictions of Unitary Representations of Real Reductive Groups

Kobayashi

Progress in Mathematics

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Cited by 27 publications

References 28 publications

Special unipotent representations of real classical groups: counting and reduction to good parity

Special unipotent representations of real classical groups: counting and reduction to good parity

One-Dimensional Representations of U (p,q) and the Howe Correspondence

Restrictions of Unitary Representations of Real Reductive Groups

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