Twisted Dirac Index and Applications to Characters

Barbasch, Dan; Pandžić, Pavle

doi:10.1007/978-3-030-32906-8_2

Cited by 10 publications

(7 citation statements)

References 31 publications

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“…This paper aims to study the Dirac series of U (p, q). The recent research announcement [4] suggests that the study here may be helpful for the theory of automorphic forms. One foundational tool for us is Theorem 1.1, the other one is Trapa's 2001 paper [25] which suggests that weakly fair A q (λ)-modules (see (16)) should play a very important role in the unitary dual of U (p, q).…”

Section: Introductionmentioning

confidence: 95%

On the Dirac Series of $U(p,q)$

Dong,

Wong

2020

Preprint

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Section: Introductionmentioning

confidence: 95%

On the Dirac Series of $U(p,q)$

Dong,

Wong

2020

Preprint

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“…Note that the latter have applications in endoscopy. In view of the research announcement by Barbasch and Pandžić [3], Dirac series should have application in the theory of automorphic forms as well.…”

Section: Introductionmentioning

confidence: 99%

Dirac series of $E_{7(-5)}$

Ding,

Dong,

2022

Preprint

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Using the sharpened Helgason-Johnson bound, this paper classifies all the irreducible unitary representations with non-zero Dirac cohomology of E 7(−5) . As an application, we find that the cancellation between the even part and the odd part of the Dirac cohomology continues to happen for certain unitary representations of E 7(−5) . Assuming the infinitesimal character being integral, we further improve the Helgason-Johnson bound for E 7(−5) . This should help people to understand (part of) the unitary dual of this group.

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“…Yet it is still worthy of pursuing since Dirac series contains many interesting unitary representations such as the discrete series [17], certain A q (λ) modules [16] and beyond. Moreover, due to the research announcement of Barbasch and Pandžić [4], Dirac series should have applications in the theory of automorphic forms.…”

Section: Introductionmentioning

confidence: 99%

Dirac index of some unitary representations of $Sp(2n, \mathbb{R})$ and $SO^*(2n)$

Dong,

Wong

2021

Preprint

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Let G be Sp(2n, R) or SO * (2n). We compute the Dirac index of a large class of unitary representations considered by Vogan in Section 8 of [32], which include all weakly fair Aq(λ) modules and (weakly) unipotent representations of G as two extreme cases. We conjecture that these representations exhaust all unitary representations of G with nonzero Dirac cohomology. In general, for certain irreducible unitary module of an equal rank group, we clarify the link between the possible cancellations in its Dirac index, and the parities of its spin-lowest K-types.

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Twisted Dirac Index and Applications to Characters

Cited by 10 publications

References 31 publications

On the Dirac Series of $U(p,q)$

On the Dirac Series of $U(p,q)$

Dirac series of $E_{7(-5)}$

Dirac index of some unitary representations of $Sp(2n, \mathbb{R})$ and $SO^*(2n)$

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