Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 9 min ago
PreprintCC BY 4.0arXiv

On the automorphisms of Pick bodies

  • Anindya Biswas
Open at sourcePDFDOICite

Abstract

We determine the biholomorphic automorphisms of the Pick body associated with finitely many distinct points in a Carathéodory hyperbolic domain. Every automorphism is the composition of a common disc automorphism applied to all coordinates and a coordinate permutation preserving the Pick body. The proof uses the quotient Banach algebra of interpolation data, its generalized von Neumann inequality, and the fact that its symmetric part consists precisely of the constant vectors. For nodes in a polydisc, we introduce minimal effective coordinate tuples and identify the admissible permutations with the automorphisms of a lower-dimensional polydisc that preserve the projected node set. This yields a direct-product description of the automorphism group, with one factor equal to the automorphism group of the disc and the other finite. We also give the resulting descriptions for nodes in the disc and the bidisc.

Related

  1. A Pick-type theorem for halfway-lattice polygons
    Charlene Chu, Yael Karshon
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsGeometry & topologyarXiv
  2. Isometric rigidity of complete Pick algebras on monomial varieties
    Hamidul Ahmed, B. Krishna Das, Chaman Kumar Sahu
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Does Calibration Pick the Right Model? Likelihood Evidence from Income Risk
    Jiuyi Cheng, Alexis Akira Toda
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  4. Bohr sets for multiplier algebras of complete Pick spaces
    Ole Fredrik Brevig, Kristian Seip, Ilya Zlotnikov
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Quantum Pick's Theorem in two dimensions
    Moris Metin Bardavid, Ruth Lawrence
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{biswas2026automorphisms,
  title = {{On the automorphisms of Pick bodies}},
  author = {Anindya Biswas},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28972},
  eprint = {2610.28972},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28972},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the automorphisms of Pick bodies
AU  - Anindya Biswas
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28972
UR  - https://arxiv.org/abs/2610.28972
AB  - We determine the biholomorphic automorphisms of the Pick body associated with finitely many distinct points in a Carathéodory hyperbolic domain. Every automorphism is the composition of a common disc automorphism applied to all coordinates and a coordinate permutation preserving the Pick body. The proof uses the quotient Banach algebra of interpolation data, its generalized von Neumann inequality, and the fact that its symmetric part consists precisely of the constant vectors. For nodes in a polydisc, we introduce minimal effective coordinate tuples and identify the admissible permutations with the automorphisms of a lower-dimensional polydisc that preserve the projected node set. This yields a direct-product description of the automorphism group, with one factor equal to the automorphism group of the disc and the other finite. We also give the resulting descriptions for nodes in the disc and the bidisc.
ER  -