标题： 与李代数相关的多项式 显示英文标题

标题： Polynomials associated to Lie algebras

摘要： 我们为半单复李代数$\mathfrak{g}$关联一个多项式序列$P_{\ell,\mathfrak{g}}(x)\in\mathbb{Q}[x]$在$r$个变量中，其中$r$是$\mathfrak{g}$的秩和$\ell=0,1,2,\ldots $。 多项式$P_{\ell,\mathfrak{g}}(x)$与$\mathfrak{g}$的同构类唯一相关，变量重命名除外，并被定义为维滕zeta函数的一种变体的特殊值。 2008年，Komori、Matsumoto 和 Tsumura 使用另一种维滕zeta函数的不同特殊值定义了与$\mathfrak{g}$相关的另一组多项式。 显示英文摘要

摘要： We associate to a semisimple complex Lie algebra $\mathfrak{g}$ a sequence of polynomials $P_{\ell,\mathfrak{g}}(x)\in\mathbb{Q}[x]$ in $r$ variables, where $r$ is the rank of $\mathfrak{g}$ and $\ell=0,1,2,\ldots $. The polynomials $P_{\ell,\mathfrak{g}}(x)$ are uniquely associated to the isomorphism class of $\mathfrak{g}$, up to re-numbering the variables, and are defined as special values of a variant of Witten's zeta function. Another set of polynomials associated to $\mathfrak{g}$ were defined in 2008 by Komori, Matsumoto and Tsumura using different special values of another variant of Witten's zeta function.