Formal degrees and adjoint -factors

@article{Hiraga2007FormalDA,
  title={Formal degrees and adjoint -factors},
  author={Kaoru Hiraga and Atsushi Ichino and Tamotsu Ikeda},
  journal={Journal of the American Mathematical Society},
  year={2007},
  volume={21},
  pages={283-304}
}
L( 12 , π1 × π0) L(1, π1, Ad)L(1, π0, Ad) if v is unramified (cf. [20]). Now let G = H×H, where H is a connected reductive algebraic group over F . For simplicity, we assume that the connected center of H is anisotropic. Let π = πH ⊗ π̌H , where πH is a discrete series representation of H and π̌H is the contragredient representation of πH . Then (0.1) can be expressed in terms of the formal degree d(πH) of πH . In this paper, we give a conjectural formula for d(πH) in terms of the adjoint… 
CORRECTION TO “FORMAL DEGREES AND ADJOINT γ-FACTORS”
The authors would like to thank Professor Gross for pointing out an error in Lemma 3.3 of [4]. Conjecture 1.4 of [4] does not hold for d(π) = d(π, μG/A,ψ) in the non-archimedean case. We need to
Correction to "Formal degrees and adjoint gamma-factors''
The authors would like to thank Professor Gross for pointing out an error in Lemma 3.3 of [4]. Conjecture 1.4 of [4] does not hold for d(π) = d(π, μG/A,ψ) in the non-archimedean case. We need to
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References

SHOWING 1-10 OF 44 REFERENCES
Haar Measure and the Artin Conductor
Let G be a connected reductive group, defined over a local, non-archimedean field k. The group G(k) is locally compact and unimodular. In [Gr], a Haar measure |ωG| was defined on G(k), using the
Twisted endoscopy and reducibility of induced representations for $p$-adic groups
1. Introduction. This is the first in a series of papers in which we study the reducibility of representations induced from discrete series representations of the Levi factors ofmaximal parabolic
Orbital Integrals in Reductive Groups
Let G be a connected reductive linear algebraic group defined over a (nondiscrete) locally compact field k of characteristic zero, and G be its group of k-rational points. If O(x) = {yxy': y e G} is
Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique
Abstract.Let F be a finite extension of ℚp. For each integer n≥1, we construct a bijection from the set ?F0(n) of isomorphism classes of irreducible degree n representations of the (absolute) Weil
Depth-zero supercuspidal L-packets and their stability
In this paper we verify the local Langlands correspondence for pure inner forms of unramied p-adic groups and tame Langlands parameters in \general position". For each such parameter, we explicitly
A proof of Langland’s conjecture on Plancherel measures; Complementary series of $p$-adic groups
analysis of p-adic reductive groups. Our first result, Theorem 7.9, proves a conjecture of Langlands on normalization of intertwining operators by means of local Langlands root numbers and
Harmonic Analysis on Real Reductive Groups III. The Maass-Selberg Relations and the Plancherel Formula
Part I. The c-, jand p-functions 2. Some elementary results on integrals 120 3. A lemma of Arthur 125 4. Induced representations 127 5. Intertwining operators 129 6. The mapping T-+XT ..131 131 7.
Some results on reducibilty for unitary groups and local Asai L-functions.
Let Fbe a/?-adic field ofcharacteristic zero and let Fbe the algebraicclosure off. In [20], Shahidi describes the relationship of the poles of certain Langlands L-functions attached to
STABLE TRACE FORMULA: CUSPIDAL TEMPERED TERMS
Consider a connected reductive group G over a number field F. For technical reasons we assume that the derived group of G is simply connected (see [L1]). in [L3] Langlands partially stabilizes the
...
1
2
3
4
5
...