Gram矩阵行列式的分解结果
Decomposition results for Gram matrix determinants
摘要：
我们研究了群$S_n,O_n,B_n,H_n$、自由群$S_n^+,O_n^+,B_n^+,H_n^+$和半自由群$O_n^*,H_n^*$的格拉姆矩阵行列式。我们首先收集所有已知的计算等决定因素，随着完整和简化的证明，并在需要的地方推广。我们推测所有这些决定因素都分解为$D=\prod_πϕ(π)$，所有相关分区上都有积。
英文摘要：
We study the Gram matrix determinants for the groups $S_n,O_n,B_n,H_n$, for their free versions $S_n^+,O_n^+,B_n^+,H_n^+$, and for the half-liberated versions $O_n^*,H_n^*$. We first collect all the known computations of such determinants, along with complete and simplified proofs, and with generalizations where needed. We conjecture that all these determinants decompose as $D=\prod_πϕ(π)$, with product over all associated partitions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
