{"paper":{"title":"The complex geomety of a domain related to $\\mu$-synthesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"J. Agler, N. J. Young, Z. A. Lykova","submitted_at":"2014-03-08T10:45:34Z","abstract_excerpt":"We describe the basic complex geometry and function theory of the {\\em pentablock} $\\mathcal{P}$, which is the bounded domain in $\\mathbb{C}^3$ given by \\[ \\mathcal{P}= \\{(a_{21}, \\mathrm{tr} A, \\det A): A= \\begin{bmatrix} a_{ij}\\end{bmatrix}_{i,j=1}^2 \\in \\mathbb{B}\\} \\] where $\\mathbb{B}$ denotes the open unit ball in the space of $2\\times 2$ complex matrices. We prove several characterizations of the domain. We describe its distinguished boundary and exhibit a $4$-parameter group of automorphisms of $\\mathcal{P}$. We show that $\\mathcal{P}$ is intimately connected with the problem of $\\mu$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1960","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"}