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Miraculous cancellations for quantum SL 2
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 3, pp. 523-557.

Des travaux précédents de Helen Wong et de l’auteur ont mis en évidence, quand le paramètre quantique q=e 2πi est une racine de l’unité, des « annulations miraculeuses » pour l’application de trace quantique qui relie l’algèbre d’écheveaux du crochet de Kauffman à l’espace de Teichmüller quantique d’une surface. L’article ci-dessous fournit une interprétation plus conceptuelle de ce phénomène, en termes de représentations du groupe quantique U q (𝔰𝔩 2 ) et de son algèbre de Hopf duale SL 2 q .

In earlier work, Helen Wong and the author discovered certain “miraculous cancellations” for the quantum trace map connecting the Kauffman bracket skein algebra of a surface to its quantum Teichmüller space, occurring when the quantum parameter q=e 2πi is a root of unity. The current paper is devoted to giving a more representation theoretic interpretation of this phenomenon, in terms of the quantum group U q (𝔰𝔩 2 ) and its dual Hopf algebra SL 2 q .

Publié le :
DOI : https://doi.org/10.5802/afst.1608
@article{AFST_2019_6_28_3_523_0,
     author = {Francis Bonahon},
     title = {Miraculous cancellations for quantum $\protect \mathrm{SL}_2$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {523--557},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 28},
     number = {3},
     year = {2019},
     doi = {10.5802/afst.1608},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1608/}
}
Francis Bonahon. Miraculous cancellations for quantum $\protect \mathrm{SL}_2$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 3, pp. 523-557. doi : 10.5802/afst.1608. https://afst.centre-mersenne.org/articles/10.5802/afst.1608/

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