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

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 .

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 .

Published online:
DOI: 10.5802/afst.1608

Francis Bonahon 1

1 Department of Mathematics, University of Southern California, Los Angeles CA 90089-2532, U.S.A.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Francis Bonahon. Miraculous cancellations for quantum $\protect \mathrm{SL}_2$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 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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