$\mathfrak{q}$-Crystal Structure on Primed Tableaux and on Signed Unimodal Factorizations of Reduced Words of Type $B$
$\mathfrak{q}$-Crystal Structure on Primed Tableaux and on Signed Unimodal Factorizations of Reduced Words of Type $B$
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$mathfrak{q}$-带底数的 Tableaux 上的晶体结构以及 $B$ 类型缩减词的有符号单峰分解
DOI：
10.4171/prims/55-2-5
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发表时间：
2018
影响因子：
1.2
通讯作者：
Toya Hiroshima
中科院分区：
文献类型：
--
作者：
Toya Hiroshima
酷儿李超代数的晶体基础理论由 Grantcharov 等人提出。结果表明，半标准分解表承认酷儿李超代数的晶体结构或简单的$\mathfrak{q}$-晶体结构。在本文中，我们探讨了底漆画面（半标准标记移位画面）的 $\mathfrak{q}$ 晶体结构以及 $B$ 类型缩减词的有符号单峰分解。我们给出了显式的奇数 Kashiwara 算子在带底数的画面上以及最高和最低权重向量的形式。我们还给出了 $B$ 类型缩减词的有符号单峰分解上奇 Kashiwara 算子的显式算法。
Crystal basis theory for the queer Lie superalgebra was developed by Grantcharov et al. and it was shown that semistandard decomposition tableaux admit the structure of crystals for the queer Lie superalgebra or simply $\mathfrak{q}$-crystal structure. In this paper, we explore the $\mathfrak{q}$-crystal structure of primed tableaux (semistandard marked shifted tableaux) and that of signed unimodal factorizations of reduced words of type $B$. We give the explicit odd Kashiwara operators on primed tableaux and the forms of the highest and lowest weight vectors. We also give the explicit algorithms for odd Kashiwara operators on signed unimodal factorizations of reduced words of type $B$.