{"paper":{"title":"Canonical factorization and diagonalization of Baxterized braid matrices: Explicit constructions and applications","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.QA","authors_text":"A. Chakrabarti","submitted_at":"2003-05-07T09:36:39Z","abstract_excerpt":"Braid matrices $\\hat{R}(\\theta)$, corresponding to vector representations, are spectrally decomposed obtaining a ratio $f_{i}(\\theta)/f_{i}(-\\theta)$ for the coefficient of each projector $P_{i}$ appearing in the decomposition. This directly yields a factorization $(F(-\\theta))^{-1}F(\\theta)$ for the braid matrix, implying also the relation $\\hat{R}(-\\theta)\\hat{R}(\\theta)=I$.This is achieved for $GL_{q}(n),SO_{q}(2n+1),SO_{q}(2n),Sp_{q}(2n)$ for all $n$ and also for various other interesting cases including the 8-vertex matrix.We explain how the limits $\\theta \\to \\pm \\infty$ can be interpret"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305103","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"}