ATOBE Hiraku Associate Professor

Research Activities

My research area is the theory of automorphic representations.
I mainly work on the local Langlands correspondence, Arthur’s multiplicity formula and liftings of automorphic representations for classical groups.

The Langlands conjecture, which is a generalization of the class field theory,
predicts a natural but mysterious correspondence between automorphic representations and Galois representations.

The local Langlands correspondence, which is a local analogue,
associates irreducible representations of reductive p-adic or Lie groups and their so-called L-parameters.

For classical groups, it was established by Arthur in 2013.
I study several notion (e.g., theta liftings, Jacquet modules) in representation theory in terms of L-parameters.

Papers:

• H. Atobe and W. T. Gan,
  Local theta correspondence of tempered representations and Langlands parameters.
  Invent. Math. 210 (2017), no. 2, 341–415.
• H. Atobe,
  On the uniqueness of generic representations in an L-packet.
  Int. Math. Res. Not. IMRN 2017, no. 23, 7051–7068.
• H. Atobe,
  The local theta correspondence and the local Gan-Gross-Prasad conjecture for the symplectic-metaplectic case.
  Math. Ann. 371 (2018), no. 1-2, 225–295.

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