The bar automorphism in quantum groups and geometry of quiver representations
Annales de l'Institut Fourier, Volume 56 (2006) no. 1, p. 255-267
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.
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.
DOI : https://doi.org/10.5802/aif.2179
Classification:  14L30,  17B37
Keywords: 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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {56},
     number = {1},
     year = {2006},
     pages = {255-267},
     doi = {10.5802/aif.2179},
     zbl = {1134.17006},
     mrnumber = {2228687},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2006__56_1_255_0}
}
The bar automorphism in quantum groups and geometry of quiver representations. Annales de l'Institut Fourier, Volume 56 (2006) no. 1, pp. 255-267. doi : 10.5802/aif.2179. https://aif.centre-mersenne.org/item/AIF_2006__56_1_255_0/

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