{"paper":{"title":"On Some Applications of Group Representation Theory to Algebraic Problems Related to the Congruence Principle for Equivariant Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hao-pin Wu, Mikhail Muzychuk, Zalman Balanov","submitted_at":"2017-06-08T20:28:06Z","abstract_excerpt":"Given a finite group $G$ and two unitary $G$-representations $V$ and $W$, possible restrictions on Brouwer degrees of equivariant maps between representation spheres $S(V)$ and $S(W)$ are usually expressed in a form of congruences modulo the greatest common divisor of lengths of orbits in $S(V)$ (denoted $\\alpha(V)$). Effective applications of these congruences is limited by answers to the following questions: (i) under which conditions, is ${\\alpha}(V)>1$? and (ii) does there exist an equivariant map with the degree easy to calculate? In the present paper, we address both questions. We show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02756","kind":"arxiv","version":1},"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"}