Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
| Autor: | Aguiar, Marcelo, Andre, Carlos, Benedetti, Carolina, Bergeron, Nantel, Chen, Zhi, Diaconis, Persi, Hendrickson, Anders, Hsiao, Samuel, Isaacs, I. Martin, Jedwab, Andrea, Johnson, Kenneth, Karaali, Gizem, Lauve, Aaron, Le, Tung, Lewis, Stephen, Li, Huilan, Magaard, Kay, Marberg, Eric, Novelli, Jean-Christophe, Pang, Amy, Saliola, Franco, Tevlin, Lenny, Thibon, Jean-Yves, Thiem, Nathaniel, Venkateswaran, Vidya, Vinroot, C. Ryan, Yan, Ning, Zabrocki, Mike |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Advances in Mathematics 229 (2012) 2310--2337 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.aim.2011.12.024 |
| Popis: | We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras. Comment: To Appear in Advances in Mathematics (2012), 23 pages |
| Databáze: | arXiv |
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