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Award ID contains: 2001257

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  1. ; (, AMERICAN MATH SOCIETY)
    Accepted Manuscript Full Text Available
  2. ; (, Tata Institute of Fundamental Research Publications)
    We prove the Chevalley restriction theorem for the commuting scheme of symplectic Lie algebras. The key step is the construction of the inverse map of the Chevalley restriction map called the spectral data map. Along the way, we establish a certain multiplicative property of the Pfaffian which is of independent interest. 
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    Accepted Manuscript Full Text Available
  3. ; (, DUKE MATHEMATICAL JOURNAL)
    Accepted Manuscript Full Text Available
  4. (, Selecta Mathematica)
    Full Text Available 
  5. (, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY)
    In this article we prove a conjecture of Braverman-Kazhdan in [BK1] on acyclicity of ρ-Bessel sheaves on reductive groups. We do so by proving a vanishing conjecture proposed in our previous work [C]. As a corollary, we obtain a geometric construction of the non-linear Fourier kernel for a finite reductive group as conjectured by Braverman and Kazhdan. The proof uses the theory of Mellin transforms, Drinfeld center of Harish-Chandra bimodules, and a construction of a class of character sheaves in mixed-characteristic. 
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