{"paper":{"title":"Real representation theory of finite categorical groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.RT","authors_text":"Matthew B. Young","submitted_at":"2018-04-24T14:00:52Z","abstract_excerpt":"We introduce and develop a categorification of the theory of Real representations of finite groups. In particular, we generalize the categorical character theory of Ganter--Kapranov and Bartlett to the Real setting. Given a Real representation of a group $\\mathsf{G}$, or more generally a finite categorical group, on a linear category, we associate a number, the modified secondary trace, to each graded commuting pair $(g, \\omega) \\in \\mathsf{G} \\times \\hat{\\mathsf{G}}$, where $\\hat{\\mathsf{G}}$ is the background Real structure on $\\mathsf{G}$. This collection of numbers defines the Real $2$-cha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09053","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"}