On geometric transfer in real twisted endoscopy

Abstract

We prove the existence of a transfer of orbital integrals in endoscopy for real reductive groups when there is twisting by an automorphism defined over the reals and by a character on the real points of the group. Our proof contains a relatively short self-contained argument for the already known case of standard endoscopy.

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      TITLE={Harmonic Analysis on Reductive {L}ie Groups},
      SERIES = {Lect. Notes in Math.},
      VOLUME={576},
      PUBLISHER = {Springer-Verlag},
      ADDRESS = {New York},
      YEAR = {1977},
      PAGES = {v+521},
      MRCLASS = {22E45},
      MRNUMBER = {0473111},
      ZBLNUMBER = {0354.43001},
      DOI = {10.1007/BFb0097814},
      MRREVIEWER = {A. U. Klimyk},
      }
  • [W1] J-L. Waldspurger, "L’endoscopie tordue n’est pas si tordue," Mem. Amer. Math. Soc., vol. 194, iss. 908, p. x, 2008.
    @article{W1,
      author={Waldspurger, J-L.},
      TITLE={L'endoscopie tordue n'est pas si tordue},
      JOURNAL = {Mem. Amer. Math. Soc.},
      FJOURNAL = {Memoirs of the American Mathematical Society},
      VOLUME = {194},
      YEAR = {2008},
      NUMBER = {908},
      PAGES = {x+261},
      ISSN = {0065-9266},
      CODEN = {MAMCAU},
      MRCLASS = {22E50 (11R34 22E35)},
      MRNUMBER = {2418405},
      ZBLNUMBER = {1146.22016},
      MRREVIEWER = {Anne-Marie H. Aubert},
      }%%%%
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    @misc{W2,
      author={Waldspurger, J-L.},
      TITLE={Errata},
      URL={http://www.math.jussieu.fr/~waldspur/},
      YEAR={2009},
     }
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    @book {Wall, MRKEY = {0929683},
      AUTHOR = {Wallach, Nolan R.},
      TITLE = {Real Reductive Groups. {I}},
      SERIES = {Pure Appl. Math.},
      VOLUME = {132},
      PUBLISHER = {Academic Press},
      ADDRESS = {Boston, MA},
      YEAR = {1988},
      PAGES = {xx+412},
      ISBN = {0-12-732960-9},
      MRCLASS = {22E46 (17B10 22-02 22E30)},
      MRNUMBER = {0929683},
      MRREVIEWER = {Roberto J. Miatello},
      ZBLNUMBER = {0666.22002},
      }
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    @book {War, MRKEY = {0499000},
      AUTHOR = {Warner, Garth},
      TITLE = {Harmonic Analysis on Semi-Simple {L}ie Groups. {II}},
      SERIES={Grundlehren Math. Wissen.},
      VOLUME={189},
      PUBLISHER = {Springer-Verlag},
      ADDRESS = {New York},
      YEAR = {1972},
      PAGES = {viii+491},
      MRCLASS = {22E45 (22E30)},
      MRNUMBER = {0499000},
      MRREVIEWER = {Mitsuo Sugiura},
      ZBLNUMBER = {0265.22021},
      }

Authors

D. Shelstad

Department of Mathematics
Rutgers University
Newark NJ 07102