Symplectic periods of the continuous spectrum of GL ( 2 n )

Shunsuke Yamana[1]

  • [1] Graduate School of Mathematics, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 4, page 1561-1580
  • ISSN: 0373-0956

Abstract

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We provide a formula for the symplectic period of an Eisenstein series on GL ( 2 n ) and determine when it is not identically zero.

How to cite

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Yamana, Shunsuke. "Symplectic periods of the continuous spectrum of $\mathrm{GL}(2n)$." Annales de l’institut Fourier 64.4 (2014): 1561-1580. <http://eudml.org/doc/275670>.

@article{Yamana2014,
abstract = {We provide a formula for the symplectic period of an Eisenstein series on $\mathrm\{GL\}(2n)$ and determine when it is not identically zero.},
affiliation = {Graduate School of Mathematics, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan},
author = {Yamana, Shunsuke},
journal = {Annales de l’institut Fourier},
keywords = {symplectic periods; intertwining periods; continuous spectrum},
language = {eng},
number = {4},
pages = {1561-1580},
publisher = {Association des Annales de l’institut Fourier},
title = {Symplectic periods of the continuous spectrum of $\mathrm\{GL\}(2n)$},
url = {http://eudml.org/doc/275670},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Yamana, Shunsuke
TI - Symplectic periods of the continuous spectrum of $\mathrm{GL}(2n)$
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 4
SP - 1561
EP - 1580
AB - We provide a formula for the symplectic period of an Eisenstein series on $\mathrm{GL}(2n)$ and determine when it is not identically zero.
LA - eng
KW - symplectic periods; intertwining periods; continuous spectrum
UR - http://eudml.org/doc/275670
ER -

References

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  1. J. Arthur, On the inner product of truncated Eisenstein series, Duke Math. J. 49 (1982), 35-70 Zbl0518.22012MR650368
  2. J. Bernstein, P -invariant distributions on GL ( N ) and the classification of unitary representations of GL ( N ) (non-archimedean case), Lie Group Representations II 1041 (1984), 50-102, Springer MR748505
  3. H. Jacquet, E. Lapid, S. Rallis, A spectral identity for skew symmetric matrices, Contributions to Automorphic Forms, Geometry, and Number Theory (2004), 421-455, Johns Hopkins University Press, Baltimore Zbl1082.11029MR2058616
  4. H. Jacquet, E. Lapid, J. Rogawski, Periods of automorphic forms, J. Am. Math. Soc. 12 (1999), 173-240 Zbl1012.11044MR1625060
  5. H. Jacquet, I.I. Piatetski-Shapiro, J. Shalika, Rankin-Selberg Convolutions, Am. J. Math. 105 (1983), 367-464 Zbl0525.22018MR701565
  6. H. Jacquet, S. Rallis, Symplectic periods, J. Reine Angew. Math. 423 (1992), 175-197 Zbl0734.11035MR1142486
  7. E. Lapid, J. Rogawski, Periods of Eisenstein series: the Galois case, Duke Math. J. 120 (2003), 153-226 Zbl1037.11033MR2010737
  8. C. Moeglin, J.-L. Waldspurger, Le spectre résiduel de GL ( n ) , Ann. Sci. École Norm. Sup. (4) 22 (1989), 605-674 Zbl0696.10023MR1026752
  9. C. Moeglin, J.-L. Waldspurger, Spectral Decomposition and Eisenstein Series, 113 (1995), Cambridge University Press Zbl0846.11032MR1361168
  10. O. Offen, On symplectic periods of discrete spectrum of GL 2 n , Israel J. Math. 154 (2006), 253-298 Zbl1148.11025MR2254544
  11. O. Offen, Residual spectrum of GL 2 n distinguished by the symplectic group, Duke Math. J. 134 (2006), 313-357 Zbl1220.11072MR2248833
  12. O. Offen, E. Sayag, On unitary representations of GL 2 n distinguished by the symplectic group, J. Number Theory 125 (2007), 344-355 Zbl1147.11028MR2332593
  13. D. Vogan, The unitary dual of GL ( n ) over an Archimedean field, Invent. Math. 83 (1986), 449-505 Zbl0598.22008MR827363

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