{"paper":{"title":"Toeplitz operators on the domain $\\{Z\\in M_{2\\times2}(\\mathbb{C}) \\mid Z Z^* < I\\}$ with $\\mathrm{U}(2)\\times\\mathbb{T}^2$-invariant symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.FA","authors_text":"Gestur Olafsson, Matthew Dawson, Raul Quiroga-Barranco","submitted_at":"2019-05-30T23:19:33Z","abstract_excerpt":"Let $D$ be the irreducible bounded symmetric domain of $2\\times2$ complex matrices that satisfy $ZZ^* < I_2$. The biholomorphism group of $D$ is realized by $\\mathrm{U}(2,2)$ with isotropy at the origin given by $\\mathrm{U}(2)\\times\\mathrm{U}(2)$. Denote by $\\mathbb{T}^2$ the subgroup of diagonal matrices in $\\mathrm{U}(2)$. We prove that the set of $\\mathrm{U}(2)\\times\\mathbb{T}^2$-invariant essentially bounded symbols yield Toeplitz operators that generate commutative $C^*$-algebras on all weighted Bergman spaces over $D$. Using tools from representation theory, we also provide an integral f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.13351","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"}