Automorphic descent for symplectic groups: The branching problems and L -functions
DOI10.1353/ajm.2023.a897497OpenAlexW4379141632MaRDI QIDQ6135854
Publication date: 28 August 2023
Published in: American Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1353/ajm.2023.a897497
Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)
Cites Work
- Poles of certain residual Eisenstein series of classical groups
- On special unipotent orbits and Fourier coefficients for automorphic forms on symplectic groups
- Multiplicity one theorems
- Multiplicity one theorems: the Archimedean case
- Eisenstein series on the metaplectic group and nonvanishing theorems for automorphic L-functions and their derivatives
- Uniqueness of Whittaker model for the metaplectic group
- On the local theta-correspondence
- Modèles de Whittaker dégénéres pour des groupes p-adiques. (Degenerate Whittaker models of p-adic groups)
- Howe correspondences on a \(p\)-adic field
- On the nonvanishing of some \(L\)-functions
- Shimura and Shintani correspondences
- On some explicit formulas in the theory of Weil representation
- On Fourier coefficients of automorphic forms of symplectic groups
- The local converse theorem for \(\operatorname {SO}(2n+1)\) and applications
- The Shimura-Waldspurger correspondence for \(\mathrm{Mp}_{2n}\)
- Automorphic integral transforms for classical groups II: twisted descents
- The local theta correspondence and the local Gan-Gross-Prasad conjecture for the symplectic-metaplectic case
- On lifting from classical groups to \(\text{GL}_N\)
- Functoriality for the classical groups
- Reductive dual pair correspondence for complex groups
- Nonvanishing theorems for automorphic \(L\)-functions on \(\text{GL} (2)\)
- On correspondences between certain automorphic forms on \(\mathrm{Sp}_{4n} (\mathbb{A})\) and \(\widetilde{\mathrm{Sp}}_{2n} (\mathbb{A})\)
- On explicit lifts of cusp forms from \(\text{GL}_m\) to classical groups
- Lifting cusp forms on \(\text{GL}_{2n}\) to \(\widetilde{\text{Sp}}_{2n}\): The unramified correspondence
- Arthur parameters and cuspidal automorphic modules of classical groups
- On the non-vanishing of the central value of certain \(L\)-functions: unitary groups
- A reciprocal branching problem for automorphic representations and global Vogan packets
- Relating invariant linear form and local epsilon factors via global methods. (With an appendix by Hiroshi Saito)
- Certain conjectures relating unipotent orbits to automorphic representations
- Nonvanishing of \(L\)-functions for \(\text{GL}(n,\mathbf A_Q)\)
- Towards a classification of global integral constructions and functorial liftings using the small representations method
- A product of tensor product \(L\)-functions of quasi-split classical groups of Hermitian type
- On the Howe correspondence for symplectic-orthogonal dual pairs
- Multiplicity one theorems for Fourier-Jacobi models
- Transcending Classical Invariant Theory
- Induced representations of reductive ${\germ p}$-adic groups. I
- $L$-functions for symplectic groups
- On a correspondence between cuspidal representations of 𝐺𝐿_{2𝑛} and 𝑆𝑝̃_{2𝑛}
- On Irreducible Representations of So2n+1 × So2m
- 𝐿 functions for the orthogonal group
- ENDOSCOPIC REPRESENTATIONS OF $\widetilde{\mathrm{Sp}}_{2n}$
- The Jacquet–Langlands Correspondence via Twisted Descent
- On the irreducibility of global descents for even unitary groups and its applications
- On the nonvanishing of the central value of the Rankin-Selberg 𝐿-functions
- Representations of metaplectic groups I: epsilon dichotomy and local Langlands correspondence
- Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
- Bessel Descents and Branching Problems
- Branching laws for classical groups: the non-tempered case
- Correspondances de Shimura et quaternions
- Endoscopic Classification of representations of Quasi-Split Unitary Groups
- Conservation relations for local theta correspondence
- On the genericity of cuspidal automorphic forms of $\mathbf{SO}\bm{(2n+1)}$, II
- Refined global Gan–Gross–Prasad conjecture for Fourier–Jacobi periods on symplectic groups
- Generalized and degenerate Whittaker models
- Raising nilpotent orbits in wave-front sets
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Automorphic descent for symplectic groups: The branching problems and L -functions