Supercharacter Theory Constructions Corresponding to Schur Ring Products

摘要

Diaconis and Isaacs have defined the supercharacter theories of a finite group to be certain approximations to the ordinary character theory of the group [77. Diaconis , P. , Isaacs , I. M. ( 2008 ). Supercharacters and superclasses for algebra groups . Trans. Amer. Math. Soc. 360 : 2359 - 2392 .[CrossRef], [Web of Science ®]View all references]. We make explicit the connection between supercharacter theories and Schur rings, and we provide supercharacter theory constructions which correspond to Schur ring products of Leung and Man [1212. Leung , K. H. , Man , S. H. ( 1996 ). On Schur rings over cyclic groups, II . J. Algebra 183 : 273 - 285 .[CrossRef], [Web of Science ®]View all references], Hirasaka and Muzychuk [1010. Hirasaka , M. , Muzychuk , M. ( 2001 ). An elementary abelian group of rank 4 is a CI-group . J. Combin. Theory Ser. A 94 : 339 - 362 .[CrossRef], [Web of Science ®]View all references], and Tamaschke [2020. Tamaschke , O. ( 1970 ). On Schur-rings which define a proper character theory on finite groups . Math. Z. 117 : 340 - 360 .[CrossRef], [Web of Science ®]View all references].View full textDownload full textKey WordsSchur rings, Supercharacters2000 Mathematics Subject Classification20C15Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927872.2011.602999