L-groups and the Langlands program for covering groups

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Author(s): Wee Teck Gan (颜维德), Fan Gao (高帆), Martin H. Weissman
Series: Astérisque 398
Publisher: Société Mathématique de France
Year: 2018

Language: English
Pages: 286

1. Generalities
2. Abstract Chevalley Groups
3. Groups over Local Fields
4. Adelic Groups
5. Brylinski-Deligne Theory
6. Representation Theory and Automorphic Forms
7. A Langlands program for Brylinski-Deligne extensions
References
Introduction
Notation
Part I. Covering groups and their L-groups
1. Covering groups
2. The dual group
3. The gerbe associated to a cover
4. The metaGalois group
5. L-groups, parameters, L-functions
Part II. Genuine representations
6. Local fields
7. Spherical representations
8. Automorphic representations
Part III. Parameters for split tori
9. A tale of two functors
10. Deligne's construction
11. Weil parameters as splittings
12. Parameterization
13. The integral case
14. Global case
15. Split tori
Part IV. Other parameterizations
16. Spherical/Unramified parameterization
17. Sharp covers of anisotropic real tori
18. Discrete series for covers of real semisimple groups
Torsors, gerbes, and fundamental groups
References
1. Introduction
2. Brylinski-Deligne Extensions
3. Topological Covering Groups
4. Tame Case
5. Dual and L-Groups
6. Distinguished Splittings of L-Groups
7. Construction of Distinguished Genuine Characters
8. LLC for Covering Tori
9. LLC for Unramified Representations
10. L-Groups: Second Take
11. The LLC
12. Desiderata and Anomalies
13. Automorphic L-functions
14. Langlands Functoriality: Base Change
15. Endoscopy
16. Examples
17. Problems and Questions
References
Summary of two constructions
1. Computations in the gerbe
2. Comparison to the second twist
References