Compatibility of the theta correspondence with the Whittaker functors
Vincent Lafforgue; Sergey Lysenko
Bulletin de la Société Mathématique de France (2011)
- Volume: 139, Issue: 1, page 75-88
- ISSN: 0037-9484
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topLafforgue, Vincent, and Lysenko, Sergey. "Compatibility of the theta correspondence with the Whittaker functors." Bulletin de la Société Mathématique de France 139.1 (2011): 75-88. <http://eudml.org/doc/272450>.
@article{Lafforgue2011,
abstract = {We prove that the global geometric theta-lifting functor for the dual pair $(H, G)$ is compatible with the Whittaker functors, where $(H,G)$ is one of the pairs $(\{\mathrm \{S\}\mathbb \{O\}\}_\{2n\}, \{\mathbb \{S\}p\}_\{2n\})$, $(\{\mathbb \{S\}p\}_\{2n\}, \{\mathrm \{S\}\mathbb \{O\}\}_\{2n+2\})$ or $(\{\mathbb \{G\}\mathrm \{L\}\}_\{n\},\{\mathbb \{G\}\mathrm \{L\}\}_\{n+1\})$. That is, the composition of the theta-lifting functor from $H$ to $G$ with the Whittaker functor for $G$ is isomorphic to the Whittaker functor for $H$.},
author = {Lafforgue, Vincent, Lysenko, Sergey},
journal = {Bulletin de la Société Mathématique de France},
keywords = {geometric Langlands; Whittaker functor; theta-lifting},
language = {eng},
number = {1},
pages = {75-88},
publisher = {Société mathématique de France},
title = {Compatibility of the theta correspondence with the Whittaker functors},
url = {http://eudml.org/doc/272450},
volume = {139},
year = {2011},
}
TY - JOUR
AU - Lafforgue, Vincent
AU - Lysenko, Sergey
TI - Compatibility of the theta correspondence with the Whittaker functors
JO - Bulletin de la Société Mathématique de France
PY - 2011
PB - Société mathématique de France
VL - 139
IS - 1
SP - 75
EP - 88
AB - We prove that the global geometric theta-lifting functor for the dual pair $(H, G)$ is compatible with the Whittaker functors, where $(H,G)$ is one of the pairs $({\mathrm {S}\mathbb {O}}_{2n}, {\mathbb {S}p}_{2n})$, $({\mathbb {S}p}_{2n}, {\mathrm {S}\mathbb {O}}_{2n+2})$ or $({\mathbb {G}\mathrm {L}}_{n},{\mathbb {G}\mathrm {L}}_{n+1})$. That is, the composition of the theta-lifting functor from $H$ to $G$ with the Whittaker functor for $G$ is isomorphic to the Whittaker functor for $H$.
LA - eng
KW - geometric Langlands; Whittaker functor; theta-lifting
UR - http://eudml.org/doc/272450
ER -
References
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