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Seminars

Seminar in Representation Theory

Fourier transform of invariant functions on a finite reductive Lie algebra

2026/07/30 (Thu.) 13:30~15:00
  • Date : 2026/07/30 (Thu.) 13:30~15:00
  • Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
  • Speaker : Wille Liu (Academia Sinica)
  • Organizer : Cheng-Chiang Tsai (AS)
  • Abstract :
    Given a connected reductive group G defined over a finite field Fq of big enough characteristic, we are interested in the Fourier transform of G(Fq)-invariant functions on the rational points of its Lie algebra g, defined as certain trigonometric sums.
    In a joint work with Cheng-Chiang Tsai and Wei-Hsuan Hsin, we show that if an invariant function on g and its Fourier transform are both supported by the nilpotent cone of g, then it is an eigenfunction for the Fourier transform with an explicit eigenvalue given by a quadratic Gauss sum.
    I'll explain the main idea of the proof, namely, lifting the problem to p-adic Lie algebras and reducing the problem to Lie algebras of smaller dimension via endoscopy.
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