Whittaker and Bessel functors for G 𝕊 p 4

Sergey Lysenko[1]

  • [1] Université Paris 6 Institut de mathématiques Analyse algébrique 175 rue du Chevaleret 75013 Paris (France)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 5, page 1505-1565
  • ISSN: 0373-0956

Abstract

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The theory of Whittaker functors for G L n is an essential technical tools in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence. We define Whittaker functors for G 𝕊 p 4 and study their properties. These functors correspond to the maximal parabolic subgroup of G 𝕊 p 4 , whose unipotent radical is not commutative.We also study similar functors corresponding to the Siegel parabolic subgroup of G 𝕊 p 4 , they are related with Bessel models for G 𝕊 p 4 and Waldspurger models for G L 2 .We define the Waldspurger category, which is a geometric counterpart of the Waldspurger module over the Hecke algebra of G L 2 . We prove a geometric version of the multiplicity one result for the Waldspurger models.

How to cite

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Lysenko, Sergey. "Whittaker and Bessel functors for $G\mathbb{S}p_4$." Annales de l’institut Fourier 56.5 (2006): 1505-1565. <http://eudml.org/doc/10183>.

@article{Lysenko2006,
abstract = {The theory of Whittaker functors for $GL_n$ is an essential technical tools in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence. We define Whittaker functors for $G\mathbb\{S\}p_4$ and study their properties. These functors correspond to the maximal parabolic subgroup of $G\mathbb\{S\}p_4$, whose unipotent radical is not commutative.We also study similar functors corresponding to the Siegel parabolic subgroup of $G\mathbb\{S\}p_4$, they are related with Bessel models for $G\mathbb\{S\}p_4$ and Waldspurger models for $GL_2$.We define the Waldspurger category, which is a geometric counterpart of the Waldspurger module over the Hecke algebra of $GL_2$. We prove a geometric version of the multiplicity one result for the Waldspurger models.},
affiliation = {Université Paris 6 Institut de mathématiques Analyse algébrique 175 rue du Chevaleret 75013 Paris (France)},
author = {Lysenko, Sergey},
journal = {Annales de l’institut Fourier},
keywords = {Geometric Langlands program; Waldspurger models; Whittaker functors; geometric Langlands program},
language = {eng},
number = {5},
pages = {1505-1565},
publisher = {Association des Annales de l’institut Fourier},
title = {Whittaker and Bessel functors for $G\mathbb\{S\}p_4$},
url = {http://eudml.org/doc/10183},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Lysenko, Sergey
TI - Whittaker and Bessel functors for $G\mathbb{S}p_4$
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 5
SP - 1505
EP - 1565
AB - The theory of Whittaker functors for $GL_n$ is an essential technical tools in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence. We define Whittaker functors for $G\mathbb{S}p_4$ and study their properties. These functors correspond to the maximal parabolic subgroup of $G\mathbb{S}p_4$, whose unipotent radical is not commutative.We also study similar functors corresponding to the Siegel parabolic subgroup of $G\mathbb{S}p_4$, they are related with Bessel models for $G\mathbb{S}p_4$ and Waldspurger models for $GL_2$.We define the Waldspurger category, which is a geometric counterpart of the Waldspurger module over the Hecke algebra of $GL_2$. We prove a geometric version of the multiplicity one result for the Waldspurger models.
LA - eng
KW - Geometric Langlands program; Waldspurger models; Whittaker functors; geometric Langlands program
UR - http://eudml.org/doc/10183
ER -

References

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  10. I. I. Piatetski-Shapiro, On the Saito-Kurokawa lifting, Invent. Math. 71 (1983), 309-338 Zbl0515.10024MR689647
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