Abstract
Henriques and Kamnitzer defined and studied a commutor for the category of crystals of a finite dimensional complex reductive Lie algebra. We show that the action of this commutor on highest weight elements can be expressed very simply using Kashiwara’s involution on the Verma crystal.
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The second author was supported by the RTG grant DMS-0354321.
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Kamnitzer, J., Tingley, P. A definition of the crystal commutor using Kashiwara’s involution. J Algebr Comb 29, 261–268 (2009). https://doi.org/10.1007/s10801-008-0136-1
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DOI: https://doi.org/10.1007/s10801-008-0136-1