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Automorphic Integral Transforms for Classical Groups II: Twisted Descents

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Representation Theory, Number Theory, and Invariant Theory

Part of the book series: Progress in Mathematics ((PM,volume 323))

Abstract

The paper (Jiang, Automorphic forms: L-functions and related geometry: assessing the legacy of I.I. Piatetski-Shapiro. Contemporary mathematics, vol 614. American Mathematical Society, Providence, RI, 2014, pp 179–242) forms Part I of the theory of Automorphic Integral Transforms for Classical Groups, where the first named author made a conjecture on how the global Arthur parameters may govern the structure of the Fourier coefficients of the automorphic representations in the corresponding global Arthur packets. This leads to a better understanding of the automorphic kernel functions with which the integral transforms yield conjecturally the endoscopic correspondences for classical groups. In this paper, we discuss the Twisted Automorphic Descent method and its variants that construct concrete modules for irreducible cuspidal automorphic representations of general classical groups. When the global Arthur parameters are generic, the details of the theory are referred to Jiang et al. (2015, accepted by IMRN), Jiang and Zhang (2015, submitted; 2015, in preparation), which extend the automorphic descent method of Ginzburg-Rallis-Soudry (The descent map from automorphic representations of GL(n) to classical groups. World Scientific, Singapore, 2011) to great generality.

Dedicated to Professor Roger Howe on the occasion of his 70th birthday

The research of the first named author is supported in part by the NSF Grants DMS–1301567, and that of the second named author is supported in part by the National University of Singapore’s start-up grant.

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Dihua Jiang

  2. Department of Mathematics, National University of Singapore, Singapore, 119076, Singapore

    Lei Zhang

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  1. Dihua Jiang
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  2. Lei Zhang
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Correspondence to Dihua Jiang .

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Editors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, OH, USA

    Jim Cogdell

  2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Ju-Lee Kim

  3. Department of Mathematics, National University of Singapore, Singapore, Singapore

    Chen-Bo Zhu

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Jiang, D., Zhang, L. (2017). Automorphic Integral Transforms for Classical Groups II: Twisted Descents. In: Cogdell, J., Kim, JL., Zhu, CB. (eds) Representation Theory, Number Theory, and Invariant Theory. Progress in Mathematics, vol 323. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59728-7_11

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