Model Transition for Representations of Unitary Type

Morimoto, Kazuki

doi:10.1093/imrn/rny048

Cited by 4 publications

(16 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us explain that this theorem follows from result in [44]. As in [44, 4.1], let Z be the unipotent subgroup of M given by Z = {m ∈ M : m i,i = 1 ∀i, m i,j = 0 if either (j > i and i + j > 2n) or (i > j and i + j ≤ 2n + 1)} and let ψ Z,F be its character…”

Section: Application Of Functional Equationsmentioning

confidence: 96%

“…Put ε 2 = ℓ M (e 1,1 +J) where e 1,1 is the matrix in Mat n with 1 in the upper left corner and zero elsewhere ε 3 = w ′ 2n,n ε 2 and ε 4 an arbitrary element of N M . As in [44,Section 9], define…”

Section: Application Of Functional Equationsmentioning

confidence: 99%

“…This element is denoted by ε ′ in the beginning of [44,Section 8] with the parameter a = − 1 2 in the notation of that paper. We also fix ε 2 = ℓ M (d) (and correspondingly…”

Section: Application Of Functional Equationsmentioning

confidence: 99%

See 2 more Smart Citations

On a certain local identity for Lapid-Mao's conjecture and formal degree conjecture : even unitary group case

Morimoto¹

2019

Preprint

Self Cite

View full text Add to dashboard Cite

Lapid and Mao formulated a conjecture on an explicit formula of Whittaker Fourier coefficients of automorphic forms on quasi-split classical groups and metaplectic groups as an analogue of Ichino-Ikeda conjecture. They also showed that this conjecture is reduced to a certain local identity in the case of unitary groups. In this paper, we study even unitary group case. Indeed, we prove this local identity over p-adic fields. Further, we prove an equivalence between this local identity and a refined formal degree conjecture over any local field of characteristic zero. As a consequence, we prove a refined formal degree conjecture over p-adic fields and we get an explicit formula of Whittaker Fourier coefficients under certain assumptions.

show abstract

Section: Application Of Functional Equationsmentioning

confidence: 96%

Section: Application Of Functional Equationsmentioning

confidence: 99%

See 1 more Smart Citation

On a certain local identity for Lapid-Mao's conjecture and formal degree conjecture : even unitary group case

Morimoto¹

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…, t then it follows from § 12.2, in its notation, that w is trivial and therefore ν − 1 2 π is tempered. When π ∈ Irr(GL 2n (E)) for some n ∈ N is such that ν − 1 2 π is tempered and GL(F)-distinguished, Morimoto proved in [33] the stronger result that LQ(π 1 0 ) is Sp-distinguished. We expect this to be true more generally, for the setting of Theorem 11.…”

Section: The Restriction Map ξ Bcmentioning

confidence: 99%

“…Acknowledgements. The authors wish to thank K. Morimoto for sharing his preprint [33] with them and Dipendra Prasad for answering their many questions. The first named author also wishes to thank Sandeep Varma for several helpful conversations and the Tata Institute of Fundamental Research, Mumbai, for providing an effective environment in which a part of this work was done.…”

mentioning

confidence: 99%

On -Distinguished Representations of the Quasi-Split Unitary Groups

Mitra¹,

Offen

2019

J. Inst. Math. Jussieu

View full text Add to dashboard Cite

We study $\text{Sp}_{2n}(F)$ -distinction for representations of the quasi-split unitary group $U_{2n}(E/F)$ in $2n$ variables with respect to a quadratic extension $E/F$ of $p$ -adic fields. A conjecture of Dijols and Prasad predicts that no tempered representation is distinguished. We verify this for a large family of representations in terms of the Mœglin–Tadić classification of the discrete series. We further study distinction for some families of non-tempered representations. In particular, we exhibit $L$ -packets with no distinguished members that transfer under base change to $\text{Sp}_{2n}(E)$ -distinguished representations of $\text{GL}_{2n}(E)$ .

show abstract

On a Certain Local Identity for Lapid–mao’s Conjecture and Formal Degree Conjecture : Even Unitary Group Case

Morimoto¹

2021

J. Inst. Math. Jussieu

Self Cite

View full text Add to dashboard Cite

Lapid and Mao formulated a conjecture on an explicit formula of Whittaker–Fourier coefficients of automorphic forms on quasi-split reductive groups and metaplectic groups as an analogue of the Ichino–Ikeda conjecture. They also showed that this conjecture is reduced to a certain local identity in the case of unitary groups. In this article, we study the even unitary-group case. Indeed, we prove this local identity over p-adic fields. Further, we prove an equivalence between this local identity and a refined formal degree conjecture over any local field of characteristic zero. As a consequence, we prove a refined formal degree conjecture over p-adic fields and get an explicit formula of Whittaker–Fourier coefficients under certain assumptions.

show abstract

Model Transition for Representations of Unitary Type

Cited by 4 publications

References 20 publications

On a certain local identity for Lapid-Mao's conjecture and formal degree conjecture : even unitary group case

On a certain local identity for Lapid-Mao's conjecture and formal degree conjecture : even unitary group case

On -Distinguished Representations of the Quasi-Split Unitary Groups

On a Certain Local Identity for Lapid–mao’s Conjecture and Formal Degree Conjecture : Even Unitary Group Case

Contact Info

Product

Resources

About