1. Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
- Author
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Aguiar, Marcelo, André, 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, and Pang, Amy
- Subjects
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SYMMETRIC functions , *MATHEMATICAL variables , *HOPF algebras , *FOURIER analysis , *GROUP theory , *FINITE fields , *ISOMORPHISM (Mathematics) , *COMBINATORICS - Abstract
Abstract: 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. [Copyright &y& Elsevier]
- Published
- 2012
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