Global $L$-packets for GSp(2) and theta lifts

By B. Roberts. Documenta Mathematica, 2001

95 citations recorded by the source corpus.

Let F be a totally real number fleld. We deflne global L-packets for GSp(2) over F which should correspond to the elliptic tem- pered admissible homomorphisms from the conjectural Langlands group of F to the L-group of GSp(2) which are reducible, or irreducible and induced from a totally real quadratic extension of F. We prove that the elements of these global L-packets occur in the space of cusp forms on GSp(2) over F as predicted by Arthur's conjecture. This can be regarded as the GSp(2) analogue of the dihedral case of the Langlands-Tunnell theorem. To obtain these results we prove a nonvanishing theorem for global theta lifts from the similitude group of a general four dimensional quadratic space over F to GSp(2) over F.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/adc0e59ff2fe705b40408b61c31debf56ed894ce

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In Applied Mathematics

1. W. Gan
2. Atsushi Ichino
3. Ralf Schmidt
4. Shuichiro Takeda
5. Tamotsu Ikeda
6. Wei Zhang
7. Paul D. Nelson

In Discrete Mathematics and Combinatorics

1. W. Gan
2. Shuichiro Takeda
3. Ralf Schmidt
4. Atsushi Ichino
5. Tamotsu Ikeda
6. Wei Zhang
7. Y. Sakellaridis
8. Paul D. Nelson

In Mathematical Physics

1. W. Gan
2. Atsushi Ichino
3. Shuichiro Takeda
4. Ralf Schmidt
5. Tamotsu Ikeda
6. Wei Zhang
7. Hiraku Atobe
8. Paul D. Nelson

Citations in the corpus

• The Local Langlands Conjecture for GSp(4) (2007, methodology): “In a more recent paper [ Ro2 ], B. Roberts has given a more detailed treatment of Vigneras’ construction of local L-packets (including the case p = 2), as well as giving a construction of the cuspidal representations associated to the analogous global L-packets and showing the Arthur multiplicity fo”
• ℓ-adic Representations Associated to Modular Forms over Imaginary Quadratic Fields (2007, unknown): “2], building on earlier work of Roberts [11, 12, 13].”
• The Saito-Kurokawa lifting and functoriality (2005, background): “The Bernstein–Zelevinski data of this representation is therefore given by [(πv ⊗ 1) ∣∣ SO(4) ] = [ν1/2πv], if πv is supercuspidal, [ξν, ξ], if πv = ξ StGL(2), [ν1/2χ, ν1/2χ−1], if πv = π(χ, χ−1).”
• On the Periods of Automorphic Forms on Special Orthogonal Groups and the Gross–Prasad Conjecture (2010, methodology): “Later, it was considered by Howe and Piatetski-Shapiro [23], Böcherer and SchulzePillot [4], Harris, Soudry, and Taylor [19], Roberts [37] more generally.”