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group determinant

群行列式

本站译名 表示论与李理论 义项编号TS-1265

英文别名
Frobenius determinant

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Introduction to Representation Theory 封面

《Introduction to Representation Theory》 · 印刷第 75 页 Section 4.10「Frobenius determinant」,Definition 4.10.1 及变量约定;本书矩阵元素取 $x_{g_i g_j}$,与通常取 $x_{g_i g_j^{-1}}$ 的约定相差列置换,行列式至多相差符号(同书第 76 页亦说明此差异)

Enumerate the elements of a finite group $G$ as follows: $g_1,g_2,\ldots,g_n$. Introduce $n$ variables indexed with the elements of $G$: $x_{g_1},x_{g_2},\ldots,x_{g_n}$. Definition 4.10.1. Consider the matrix $X_G$ with entries $a_{ij}=x_{g_i g_j}$. The determinant of $X_G$ is some polynomial of degree $n$ of $x_{g_1},x_{g_2},\ldots,x_{g_n}$ that is called the Frobenius determinant, or group determinant.

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