We provide a characterization of the crystal bases for the quantum queer superalgebra recently introduced by Grantcharov et al. This characterization is a combination of local queer axioms generalizing Stembridge's local axioms for crystal bases for simply-laced root systems, which were recently introduced by Assaf and Oguz, with further axioms and a new graph G characterizing the relations of the type A components of the queer supercrystal. We provide a counterexample to Assaf's and Oguz' conjecture that the local queer axioms uniquely characterize the queer supercrystal. We obtain a combinatorial description of the graph G on the type A components by providing explicit combinatorial rules for the odd queer operators on certain highest weight elements. This also yields a new combinatorial description of the Schur expansion of the Schur P-polynomials.

我们提供了Grantcharov等人最近引入的量子酷儿超级代数的晶体基础的表征。此特征是局部奇异公理的组合，该局部奇异公理推广了简单带根系统的晶体基底的Stembridge局部公理（最近由Assaf和Oguz引入），进一步的公理和新图形G表征了特征A型成分之间的关系。奇怪的超晶。我们为阿萨夫（Assaf）和奥古兹（Oguz）的猜想提供了一个反例，即当地的酷儿公理是酷儿超晶的唯一特征。我们获得了关于类型A的图G的组合描述通过为某些最高权重元素上的奇数酷儿运算符提供显式组合规则来组成组件。这也产生了Schur P多项式的Schur展开的新组合描述。