Open Access
December 2010 Quantum queer superalgebra and crystal bases
Dimitar Grantcharov, Ji Hye Jung, Seok-Jin Kang, Masaki Kashiwara, Myungho Kim
Proc. Japan Acad. Ser. A Math. Sci. 86(10): 177-182 (December 2010). DOI: 10.3792/pjaa.86.177


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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Dimitar Grantcharov. Ji Hye Jung. Seok-Jin Kang. Masaki Kashiwara. Myungho Kim. "Quantum queer superalgebra and crystal bases." Proc. Japan Acad. Ser. A Math. Sci. 86 (10) 177 - 182, December 2010.


Published: December 2010
First available in Project Euclid: 6 December 2010

zbMATH: 1237.17018
MathSciNet: MR2752232
Digital Object Identifier: 10.3792/pjaa.86.177

Primary: 17B37 , 81R50

Keywords: Crystal bases , odd Kashiwara operators , Quantum queer superalgebra

Rights: Copyright © 2010 The Japan Academy

Vol.86 • No. 10 • December 2010
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