In this paper, we develop the crystal basis theory for the quantum queer superalgebra . We define the notion of crystal bases and prove the tensor product rule for -modules in the category . Our main theorem shows that every -module in the category has a unique crystal basis.
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Dimitar Grantcharov, Ji Hye Jung, Seok-Jin Kang, Masaki Kashiwara, Myungho Kim, Crystal bases for the quantum queer superalgebra. J. Eur. Math. Soc. 17 (2015), no. 7, pp. 1593–1627DOI 10.4171/JEMS/540