Normal supercharacter theories and their supercharacters

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• 作者：Farid Aliniaeifard ^{faridanf@mathstat.yorku.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：20C12 ; 20E15 ; 05E10
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：469
• 期：Complete
• 页码：464-484
• 全文大小：385 K

文摘

In order to find a tractable theory to substitute for the wild character theory of the group of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316303076&_mathId=si1.gif&_user=111111111&_pii=S0021869316303076&_rdoc=1&_issn=00218693&md5=c60284d94062706ba5b0d032ebc2e18f" title="Click to view the MathML source">n×nclass="mathContainer hidden">class="mathCode">$n\times n$ unipotent upper-triangular matrices over a finite field class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316303076&_mathId=si2.gif&_user=111111111&_pii=S0021869316303076&_rdoc=1&_issn=00218693&md5=b0c35a30f1c995435c41fc94bcab3fcf" title="Click to view the MathML source">F_qclass="mathContainer hidden">class="mathCode">${\mathbb{F}}_q$, André and Yan introduced the notion of supercharacter theory. In this paper, we construct a supercharacter theory from an arbitrary set S of normal subgroups of G. We call such supercharacter theory the normal supercharacter theory generated by S. It is shown that normal supercharacter theories are integral, and a recursive formula for supercharacters of the normal supercharacter theory is provided. Also, we indicate that the superclasses of the normal supercharacter theory generated by all normal subgroups of G are given by certain values on the primitive central idempotents. We study the connection between the finest normal supercharacter theory and faithful irreducible characters. Moreover, an algorithm is presented to construct the supercharacter table of the finest normal supercharacter theory from the character table. Finally, we argue that normal supercharacter theories cannot be obtained by previously known supercharacter theory constructions.