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The local Langlands conjecture for p-adic GSpin4, GSpin6, and their inner forms

  • Mahdi Asgari EMAIL logo and Kwangho Choiy
Published/Copyright: January 19, 2017
Forum Mathematicum
From the journal Forum Mathematicum Volume 29 Issue 6

Abstract

We establish the local Langlands conjecture for small rank general spin groups GSpin4 and GSpin6 as well as their inner forms. We construct appropriate L-packets and prove that these L-packets satisfy the properties expected of them to the extent that the corresponding local factors are available. We are also able to determine the exact sizes of the L-packets in many cases.

Keywords: inner form; general spin group; restriction of representations; equality of local factors
MSC 2010: 22E50; 11S37; 20G25; 22E35

Communicated by Freydoon Shahidi

Funding source: Simons Foundation

Award Identifier / Grant number: 245422

Funding statement: The first author was partially supported by a Collaborations Grant (#245422) from the Simons Foundation. The second author was partially supported by an AMS-Simons Travel Grant.

Acknowledgements

This work has benefited from many helpful conversations with Wee Teck Gan and the authors would like to thank him for all his help. The authors also thank Maarten Solleveld for his feedback and comments on this work. We also thank the referee for helpful comments.

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Received: 2016-10-11
Revised: 2016-12-24
Published Online: 2017-1-19
Published in Print: 2017-11-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. The role of the Rogers–Shephard inequality in the characterization of the difference body
  3. Test vectors for local periods
  4. The local Langlands conjecture for p-adic GSpin4, GSpin6, and their inner forms
  5. A family of irretractable square-free solutions of the Yang–Baxter equation
  6. On Sylow permutable subgroups of finite groups
  7. Using Steinberg algebras to study decomposability of Leavitt path algebras
  8. The ℓ∞-semi-norm on uniformly finite homology
  9. Minimal potential results for Schrödinger equations with Neumann boundary conditions
  10. On a unique continuation for Aharonov–Bohm magnetic Schrödinger equation
  11. Sup-norm bounds for Eisenstein series
  12. Permutohedral structures on E2-operads
  13. On the complete integrability of the periodic quantum Toda lattice
  14. Fans, decision problems and generators of free abelian ℓ-groups
  15. Standard cocycles: Variations on themes of C. Kassel’s and R. Wilson’s
  16. Crossed modules as maps between connected components of topological groups
  17. A local converse theorem for U(2,2)
  18. Probabilistic trace and Poisson summation formulae on locally compact abelian groups
https://doi.org/10.1515/forum-2016-0213
Keywords for this article
inner form; general spin group; restriction of representations; equality of local factors

Articles in the same Issue

  1. Frontmatter
  2. The role of the Rogers–Shephard inequality in the characterization of the difference body
  3. Test vectors for local periods
  4. The local Langlands conjecture for p-adic GSpin4, GSpin6, and their inner forms
  5. A family of irretractable square-free solutions of the Yang–Baxter equation
  6. On Sylow permutable subgroups of finite groups
  7. Using Steinberg algebras to study decomposability of Leavitt path algebras
  8. The ℓ∞-semi-norm on uniformly finite homology
  9. Minimal potential results for Schrödinger equations with Neumann boundary conditions
  10. On a unique continuation for Aharonov–Bohm magnetic Schrödinger equation
  11. Sup-norm bounds for Eisenstein series
  12. Permutohedral structures on E2-operads
  13. On the complete integrability of the periodic quantum Toda lattice
  14. Fans, decision problems and generators of free abelian ℓ-groups
  15. Standard cocycles: Variations on themes of C. Kassel’s and R. Wilson’s
  16. Crossed modules as maps between connected components of topological groups
  17. A local converse theorem for U(2,2)
  18. Probabilistic trace and Poisson summation formulae on locally compact abelian groups
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