The bar automorphism in quantum groups and geometry of quiver representations
[L’automorphisme barre des groupes quantiques et géométrie des représentations de carquois]
Caldero, Philippe ; Reineke, Markus
Annales de l'Institut Fourier, Tome 56 (2006), p. 255-267 / Harvested from Numdam
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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.

Publié le : 2006-01-01
DOI : https://doi.org/10.5802/aif.2179
Classification:  14L30,  17B37 
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     author = {Caldero, Philippe and Reineke, Markus},
     title = {The bar automorphism in quantum groups and geometry of quiver representations},
     journal = {Annales de l'Institut Fourier},
     volume = {56},
     year = {2006},
     pages = {255-267},
     doi = {10.5802/aif.2179},
     zbl = {1134.17006},
     mrnumber = {2228687},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 255-267. doi : 10.5802/aif.2179. http://gdmltest.u-ga.fr/item/AIF_2006__56_1_255_0/

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