{"paper":{"title":"Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Aaron Lauve, Amy Pang, Anders Hendrickson, Andrea Jedwab, Carlos Andre, Carolina Benedetti, C. Ryan Vinroot, Eric Marberg, Franco Saliola, Gizem Karaali, Huilan Li, I. Martin Isaacs, Jean-Christophe Novelli, Jean-Yves Thibon, Kay Magaard, Kenneth Johnson, Lenny Tevlin, Marcelo Aguiar, Mike Zabrocki, Nantel Bergeron, Nathaniel Thiem, Ning Yan, Persi Diaconis, Samuel Hsiao, Stephen Lewis, Tung Le, Vidya Venkateswaran, Zhi Chen","submitted_at":"2010-09-21T16:29:24Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4134","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}