Supercharacter Theory Constructions Corresponding to Schur Ring Products

REFERENCES

• Aguiar , M. , Andre , C. , Benedetti , C. , Bergeron , N. , Chen , Z. , Diaconis , P. , Hendrickson , A. , Hsiao , S. , Isaacs , I. M. , Jedwab , A. , Johnson , K. , Karaali , G. , Lauve , A. , Le , T. , Lewis , S. , Li , H. , Magaard , K. , Marberg , E. , Novelli , J.-C. , Pang , A. , Saliola , F. , Tevlin , L. , Thibon , J.-Y. , Thiem , N. , Venkateswaran , V. , Vinroot , C. R. , Yan , N. , Zabrocki , M. ( 2012 ). Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras . Adv. Math. 229 : 2310 – 2337 .
   Web of Science ®Google Scholar
• André , C. A. M. ( 1995 ). Basic characters of the unitriangular group . J. Algebra 175 : 287 – 319 .
   Web of Science ®Google Scholar
• André , C. A. M. ( 1999 ). Irreducible characters of finite algebra groups. In: Matrices and Group Representations (Coimbra, 1998). Vol. 19, of Textos Mat. Sér. B, Coimbra, Portugal: University of Coimbra, pp. 65–80 .
   Google Scholar
• André , C. A. M. ( 2002 ). Basic characters of the unitriangular group (for arbitrary primes) . Proc. Amer. Math. Soc. 130 : 1943 – 1954 .
   Web of Science ®Google Scholar
• Arias-Castro , E. , Diaconis , P. , Stanley , R. (2004). A super-class walk on upper-triangular matrices. J. Algebra 278:739–765.
   Web of Science ®Google Scholar
• Bailey , R. A. , Cameron , P. J. ( 2005 ). Crested products of association schemes . J. London Math. Soc. 72 : 1 – 24 .
   Web of Science ®Google Scholar
• Diaconis , P. , Isaacs , I. M. ( 2008 ). Supercharacters and superclasses for algebra groups . Trans. Amer. Math. Soc. 360 : 2359 – 2392 .
   Web of Science ®Google Scholar
• Evdokimov , S. , Ponomarenko , I. ( 2001 ). On a family of Schur rings over a finite cyclic group . Algebra Anal. 13(3):139–154. English translation in St. Petersburg Math. J. 13 : 441 – 451 .
   Google Scholar
• Hendrickson , A. O. F. ( 2008 ). Supercharacter Theories of Finite Cyclic Groups. Ph.D., dissertation, University of Wisconsin–Madison .
   Google Scholar
• Hirasaka , M. , Muzychuk , M. ( 2001 ). An elementary abelian group of rank 4 is a CI-group . J. Combin. Theory Ser. A 94 : 339 – 362 .
   Web of Science ®Google Scholar
• Humphries , S. P. , Johnson , K. W. ( 2008 ). Fusions of character tables and Schur rings of abelian groups . Comm. Algebra 36 : 1437 – 1460 .
   Web of Science ®Google Scholar
• Leung , K. H. , Man , S. H. ( 1996 ). On Schur rings over cyclic groups, II . J. Algebra 183 : 273 – 285 .
   Web of Science ®Google Scholar
• Leung , K. H. , Man , S. H. ( 1998 ). On Schur rings over cyclic groups . Israel J. Math. 106 : 251 – 267 .
   Web of Science ®Google Scholar
• Marberg , E. ( 2011 ). A supercharacter analogue for normality . J. Algebra 332 : 334 – 365 .
   Web of Science ®Google Scholar
• Marberg , E. , Thiem , N. ( 2009 ). Superinduction for pattern groups . J. Algebra 321 : 3681 – 3703 .
   Web of Science ®Google Scholar
• Muzychuk , M. ( 2009 ). A wedge product of association schemes . European J. Combin. 30 : 705 – 715 .
   Web of Science ®Google Scholar
• Muzychuk , M. , Ponomarenko , I. ( 2009 ). Schur rings . European J. Combin. 30 : 1526 – 1539 .
   Web of Science ®Google Scholar
• Schur , I. ( 1933 ). Zur Theorie der einfach transitiven Permutationsgruppen. Sitzungsber. Preuss. Akad. Wiss. Phys.-Math. Kl. pp. 598–623 .
   Google Scholar
• Scott , W. R. ( 1987 ). Group Theory . New York : Dover .
   Google Scholar
• Tamaschke , O. ( 1970 ). On Schur-rings which define a proper character theory on finite groups . Math. Z. 117 : 340 – 360 .
   Web of Science ®Google Scholar
• Thiem , N. Branching rules in the ring of superclass functions of unipotent upper-triangular matrices . J. Algebraic Combin.
   Web of Science ®Google Scholar
• Wielandt , H. ( 1964 ). Finite Permutation Groups . New York : Academic Press .
   Google Scholar
• Yan , N. ( 2001 ). Representation Theory of the Finite Unipotent Linear Groups. Ph.D. dissertation, University of Pennsylvania. arXiv:1004.2674v1 [math.RT] .
   Google Scholar
• Communicated by A. Turull.
   Google Scholar