Abstract
We prove a local converse theorem for
Funding source: Simons Foundation
Award Identifier / Grant number: 422638
Award Identifier / Grant number: 584704
Funding statement: The first-named author was partially supported by the Simons Foundation Collaboration Grant 422638 and by a PSC-CUNY award, jointly funded by the Professional Staff Congress and The City University of New York. The second-named author was partially supported by the Simons Foundation Collaboration Grant 584704.
Acknowledgements
We thank Hervé Jacquet for suggesting this problem. We also thank the anonymous referee for his/her valuable comments.
References
[1]
M. Adrian, B. Liu, S. Stevens and P. Xu,
On the Jacquet conjecture on the local converse problem for p-adic
[2]
M. Adrian and S. Takeda,
On local L-factors for Archimedean
[3] J. Chai, Bessel functions and local converse conjecture of Jacquet, J. Eur. Math. Soc. (JEMS) 21 (2019), no. 6, 1703–1728. Search in Google Scholar
[4]
J.-P. J. Chen,
The
[5] G. Henniart, Caractérisation de la correspondance de Langlands locale par les facteurs ϵ de paires, Invent. Math. 113 (1993), no. 2, 339–350. Search in Google Scholar
[6]
G. Henniart,
Une caractérisation de la correspondance de Langlands locale pour
[7] H. Jacquet, Archimedean Rankin–Selberg integrals, Automorphic Forms and L-Functions II. Local Aspects, Contemp. Math. 489, American Mathematical Society, Providence (2009), 57–172. Search in Google Scholar
[8]
H. Jacquet and R. P. Langlands,
Automorphic Forms on
[9]
H. Jacquet and B. Liu,
On the local converse theorem for p-adic
[10]
D. Jiang, C. Nien and S. Stevens,
Towards the Jacquet conjecture on the local converse problem for p-adic
[11] R. P. Langlands, On the classification of irreducible representations of real algebraic groups, Representation Theory and Harmonic Analysis on Semisimple Lie Groups, Math. Surveys Monogr. 31, American Mathematical Society, Providence (1989), 101–170. Search in Google Scholar
[12]
C. Moeglin,
Representations of
[13] C. Nien, A proof of the finite field analogue of Jacquet’s conjecture, Amer. J. Math. 136 (2014), no. 3, 653–674. Search in Google Scholar
[14] F. Shahidi, Local coefficients as Artin factors for real groups, Duke Math. J. 52 (1985), no. 4, 973–1007. Search in Google Scholar
[15] B. Speh and D. A. Vogan, Jr., Reducibility of generalized principal series representations, Acta Math. 145 (1980), no. 3–4, 227–299. Search in Google Scholar
[16] N. R. Wallach, Real Reductive Groups. II, Pure Appl. Math. 132, Academic Press, Boston, 1992. Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- The theta cycles for modular forms modulo prime powers
- Relations among Ramanujan-type congruences II: Ramanujan-type congruences in half-integral weights
- A unified approach to Gelfand and de Vries dualities
- The cardinality of orthogonal exponentials of planar self-affine measures with two-element digit set
- Categorically closed countable semigroups
- Symmetric skew braces and brace systems
- A new class of uncertainty principles for the k-Hankel wavelet transform
- Homogeneous ACM bundles on isotropic Grassmannians
- On the global L 2-boundedness of Fourier integral operators with rough amplitude and phase functions
- A local converse theorem for Archimedean GL(n)
- Fractional Bloom boundedness and compactness of commutators
- A Mikhlin-type multiplier theorem for the partial harmonic oscillator
- Rational pullbacks of toric foliations
- On fractional integrals generated by Radon transforms over paraboloids
Articles in the same Issue
- Frontmatter
- The theta cycles for modular forms modulo prime powers
- Relations among Ramanujan-type congruences II: Ramanujan-type congruences in half-integral weights
- A unified approach to Gelfand and de Vries dualities
- The cardinality of orthogonal exponentials of planar self-affine measures with two-element digit set
- Categorically closed countable semigroups
- Symmetric skew braces and brace systems
- A new class of uncertainty principles for the k-Hankel wavelet transform
- Homogeneous ACM bundles on isotropic Grassmannians
- On the global L 2-boundedness of Fourier integral operators with rough amplitude and phase functions
- A local converse theorem for Archimedean GL(n)
- Fractional Bloom boundedness and compactness of commutators
- A Mikhlin-type multiplier theorem for the partial harmonic oscillator
- Rational pullbacks of toric foliations
- On fractional integrals generated by Radon transforms over paraboloids