Aguiar, Marcelo and André, Carlos and Benedetti, Carolina and Bergeron, Nantel and Chen, Zhi et al. - Supercharacters, symmetric functions in noncommuting variables (extended abstract)

dmtcs:2967 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Supercharacters, symmetric functions in noncommuting variables (extended abstract)

Authors: Aguiar, Marcelo and André, Carlos and Benedetti, Carolina and Bergeron, Nantel and Chen, Zhi and Diaconis, Persi and Hendrickson, Anders and Hsiao, Samuel and Isaacs, I. Martin and Jedwab, Andrea and Johnson, Kenneth and Karaali, Gizem and Lauve, Aaron and Le, Tung and Lewis, Stephen and Li, Huilan and Magaard, Kay and Marberg, Eric and Novelli, Jean-Christophe and Pang, Amy and Saliola, Franco and Tevlin, Lenny and Thibon, Jean-Yves and Thiem, Nathaniel and Venkateswaran, Vidya and Vinroot, C. Ryan and Yan, Ning and Zabrocki, Mike

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.


Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Submitted on: January 31, 2017
Keywords: supercharacters, set partitions, symmetric functions in non-commuting variables, Hopf algebras,[INFO] Computer Science [cs],[MATH] Mathematics [math]


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