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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Cai, L. and Xu, B. 2014. Residues of Intertwining Operators for U(3,3) and Base Change. International Mathematics Research Notices,


    Yu, Xiaoxiang and Wang, Dengyin 2013. Norm correspondence on p-adic classical groups. Journal of Algebra, Vol. 378, p. 22.


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Residues of intertwining operators for SO*6 as character identities

  • Freydoon Shahidi (a1) and Steven Spallone (a2)
  • DOI: http://dx.doi.org/10.1112/S0010437X09004515
  • Published online: 20 April 2010
Abstract
Abstract

We show that the residue at s=0 of the standard intertwining operator attached to a supercuspidal representation πχ of the Levi subgroup GL2(FE1 of the quasisplit group SO*6(F) defined by a quadratic extension E/F of p-adic fields is proportional to the pairing of the characters of these representations considered on the graph of the norm map of Kottwitz–Shelstad. Here π is self-dual, and the norm is simply that of Hilbert’s theorem 90. The pairing can be carried over to a pairing between the character on E1 and the character on E× defining the representation of GL2(F) when the central character of the representation is quadratic, but non-trivial, through the character identities of Labesse–Langlands. If the quadratic extension defining the representation on GL2(F) is different from E the residue is then zero. On the other hand when the central character is trivial the residue is never zero. The results agree completely with the theory of twisted endoscopy and L-functions and determines fully the reducibility of corresponding induced representations for all s.

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[21]F. Shahidi , Twisted endoscopy and reducibility of induced representations for p-adic groups, Duke Math. J. 66 (1992), 141.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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