Proceedings of the Japan Academy, Series A, Mathematical Sciences

Quantum queer superalgebra and crystal bases

Dimitar Grantcharov, Ji Hye Jung, Seok-Jin Kang, Masaki Kashiwara, and Myungho Kim

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In this paper, we develop the crystal basis theory for the quantum queer superalgebra $U_{q}(\mathfrak{q}(n))$. We define the notion of crystal bases, describe the tensor product rule, and present the existence and uniqueness of crystal bases for $U_{q}(\mathfrak{q}(n))$-modules in the category $\mathcal{O}_{\textit{int}}^{\ge 0}$.

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Proc. Japan Acad. Ser. A Math. Sci. Volume 86, Number 10 (2010), 177-182.

First available in Project Euclid: 6 December 2010

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Primary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23] 81R50: Quantum groups and related algebraic methods [See also 16T20, 17B37]

Quantum queer superalgebra crystal bases odd Kashiwara operators


Grantcharov, Dimitar; Jung, Ji Hye; Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho. Quantum queer superalgebra and crystal bases. Proceedings of the Japan Academy, Series A, Mathematical Sciences 86 (2010), no. 10, 177--182. doi:10.3792/pjaa.86.177.

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