Geodesic
The crystal commutor and Drinfeld's unitarized $R$-matrix
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 3, pp. 315-335.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Drinfeld defined a unitarized R-matrix for any quantum group $U _{ q}(\mathfrak g)$ U_q($\mathfrak $g) . This gives a commutor for the category of $U _{ q}(\mathfrak g)$ U_q($\mathfrak $g) representations, making it into a coboundary category. Henriques and Kamnitzer defined another commutor which also gives $U _{ q}(\mathfrak g)$ U_q($\mathfrak $g) representations the structure of a coboundary category. We show that a particular case of Henriques and Kamnitzer's construction agrees with Drinfeld's commutor. We then describe the action of Drinfeld's commutor on a tensor product of two crystal bases, and explain the relation to the crystal commutor.
Keywords: keywords coboundary category, quantum group, R-matrix, crystal basis 
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     author = {Kamnitzer, Joel and Tingley, Peter},
     title = {The crystal commutor and {Drinfeld's} unitarized $R$-matrix},
     journal = {Journal of Algebraic Combinatorics},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2009__29_3_a3/}
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Kamnitzer, Joel; Tingley, Peter. The crystal commutor and Drinfeld's unitarized $R$-matrix. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 3, pp. 315-335. http://geodesic.mathdoc.fr/item/JAC_2009__29_3_a3/