[L’automorphisme barre des groupes quantiques et géométrie des représentations de carquois]
On donne deux interprétations géométriques de l’automorphisme barre de la partie positive d’une algèbre enveloppante quantique. La première est en terme de nombre de points rationnels sur des corps finis d’analogues de variétés orbitales en théorie des carquois. La seconde est en terme de dualité dans les fonctions constructibles sur la variéte préprojective.
Two geometric interpretations of the bar automorphism in the positive part of a quantized enveloping algebra are given. The first is in terms of numbers of rational points over finite fields of quiver analogues of orbital varieties; the second is in terms of a duality of constructible functions provided by preprojective varieties of quivers.
Mots clés : quantum groups, quiver representations, bar automorphism, preprojective variety
@article{AIF_2006__56_1_255_0,
author = {Caldero, Philippe and Reineke, Markus},
title = {The bar automorphism in quantum groups and geometry of quiver representations},
journal = {Annales de l'Institut Fourier},
pages = {255--267},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {56},
number = {1},
year = {2006},
doi = {10.5802/aif.2179},
zbl = {1134.17006},
mrnumber = {2228687},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2179/}
}
TY - JOUR AU - Caldero, Philippe AU - Reineke, Markus TI - The bar automorphism in quantum groups and geometry of quiver representations JO - Annales de l'Institut Fourier PY - 2006 SP - 255 EP - 267 VL - 56 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2179/ DO - 10.5802/aif.2179 LA - en ID - AIF_2006__56_1_255_0 ER -
%0 Journal Article %A Caldero, Philippe %A Reineke, Markus %T The bar automorphism in quantum groups and geometry of quiver representations %J Annales de l'Institut Fourier %D 2006 %P 255-267 %V 56 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2179/ %R 10.5802/aif.2179 %G en %F AIF_2006__56_1_255_0
Caldero, Philippe; Reineke, Markus. The bar automorphism in quantum groups and geometry of quiver representations. Annales de l'Institut Fourier, Tome 56 (2006) no. 1, pp. 255-267. doi : 10.5802/aif.2179. http://www.numdam.org/articles/10.5802/aif.2179/
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