Quantum queer superalgebra and crystal bases

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Dimitar Grantcharov¹  Ji Hye Jung²  Seok-Jin Kang³  Masaki Kashiwara³  Myungho Kim² 

[1] Department of Mathematics, University of Texas at Arlington;Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University;Research Institute for Mathematical Sciences, Kyoto University

关键词: Quantum queer superalgebra;    crystal bases;    odd Kashiwara operators.;   

DOI  :  10.3792/pjaa.86.177

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

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 $\mathcal{O}_{\textit{int}}^{\ge 0}$.

【 授权许可】

Unknown