The crystal commutor and Drinfeld's unitarized R-matrix

Details The crystal commutor and Drinfeld's unitarized R-matrix The crystal commutor and Drinfeld's unitarized R-matrix

2007-07-16

arxiv.org/abs/0707.2248v2

Mathematics

Quantum Algebra

15 pages

Scientific paper

Drinfeld defined a unitarized R-matrix for any quantum group U_q(g). This gives a commutor for the category of U_q(g) representations, making it into a coboundary category. Henriques and Kamnitzer defined another commutor which also gives U_q(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.

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