queer李超代数的牛顿恒等式与有限秩重构
A Newton Identity and Finite-Rank Reconstruction for the Queer Lie Superalgebra
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中文总结 AI 辅助
本文针对queer李超代数$\frak q_N$建立牛顿型恒等式，推导生成元变换、行列式关系与重构定理，明确中心生成元并刻画一般中心特征。
中文摘要 AI 辅助
我们为queer李超代数$\boldsymbol{\frak q}_N$建立了牛顿型恒等式，将Sergeev的奇循环中心元素与Nazarov的单行Capelli元素关联起来。该恒等式通过比较Ivanov的阶乘Schur Q-函数生成函数与Grigoryev和Nazarov的queer Perelomov-Popov乘积得到。其系数展开产生了奇循环族与奇单行族之间的三角生成元变换。特别地，奇单行Capelli元素生成中心，而偶单行元素是冗余的。在固定秩下，我们推导了行列式关系和一般重构定理。基本循环Hankel行列式被识别为结式，并分解为强典型性失效因子和移位共振因子。在该行列式处局部化后，中心由前$2N$个奇循环元素生成；因此，一般中心特征由其在这些元素上的值决定。
英文摘要
We establish a Newton-type identity for the queer Lie superalgebra $\mathfrak q_N$, relating Sergeev's odd cyclic central elements to Nazarov's one-row Capelli elements. The identity is obtained by comparing Ivanov's generating function for factorial Schur $Q$-functions with the queer Perelomov-Popov product of Grigoryev and Nazarov. Its coefficient expansion yields a triangular change of generators between the odd cyclic and odd one-row families. In particular, the odd one-row Capelli elements generate the center, while the even one-row elements are redundant. In fixed rank, we derive determinantal relations and a generic reconstruction theorem. The basic cyclic Hankel determinant is identified with a resultant and factored into the failure-of-strong-typicality and shifted-resonance factors. After localization at this determinant, the center is generated by the first $2N$ odd cyclic elements; consequently, generic central characters are determined by their values on these elements.
