A generalization of immanants based on partition algebra characters

John M. Campbell
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Abstract

We introduce a generalization of immanants of matrices, using partition algebra characters in place of symmetric group characters. We prove that our immanant-like function on square matrices, which we refer to as the recombinant, agrees with the usual definition for immanants for the special case whereby the vacillating tableaux associated with the irreducible characters correspond, according to the Bratteli diagram for partition algebra representations, to the integer partition shapes for symmetric group characters. In contrast to previously studied variants and generalizations of immanants, as in Temperley–Lieb immanants and f-immanants, the sum that we use to define recombinants is indexed by a full set of partition diagrams, as opposed to permutations.

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基于分区代数字符的常量概化
我们用分割代数字符代替对称群字符,引入了矩阵高程的一般化。我们证明,我们在正方形矩阵上的伊曼函数--我们称之为重组函数--在特殊情况下与伊曼的通常定义一致,在这种情况下,与不可还原字符相关的空位表象,根据分割代数表示的布拉泰利图,对应于对称群字符的整数分割形状。与之前研究过的 "訇 "的变体和概括(如滕伯里-李布 "訇 "和 f-"訇")不同,我们用来定义重组子的和是以一整套分区图为索引的,而不是以排列为索引的。
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