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