{"paper":{"title":"Walks on Graphs and Their Connections with Tensor Invariants and Centralizer Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dongho Moon, Georgia Benkart","submitted_at":"2016-10-25T11:36:02Z","abstract_excerpt":"The number of walks of $k$ steps from the node $\\mathsf{0}$ to the node $\\lambda$ on the representation graph (McKay quiver) determined by a finite group $\\mathsf{G}$ and a $\\mathsf{G}$-module $\\mathsf{V}$ is the multiplicity of the irreducible $\\mathsf{G}$-module $\\mathsf{G}_\\lambda$ in the tensor power $\\mathsf{V}^{\\otimes k}$, and it is also the dimension of the irreducible module labeled by $\\lambda$ for the centralizer algebra $\\mathsf{Z}_k(\\mathsf{G}) = {\\mathsf{End}}_\\mathsf{G}(\\mathsf{V}^{\\otimes k})$. This paper explores ways to effectively calculate that number using the character th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07837","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"}