Arithmetic invariants of discrete Langlands parameters

@article{Gross2010ArithmeticIO,
  title={Arithmetic invariants of discrete Langlands parameters},
  author={B. Gross and Mark Reeder},
  journal={Duke Mathematical Journal},
  year={2010},
  volume={154},
  pages={431-508}
}
Let G be a reductive algebraic group over the local field k. The local Langlands conjecture predicts that the irreducible complex representations π of the locally compact group G(k) can be parametrized by objects of an arithmetic nature: homomorphisms φ from the Weil-Deligne group of k to the complex L-group of G, together with an irreducible representation ρ of the component group of the centralizer of φ. In light of this conjecture which has been established for algebraic tori, as well as for… 
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