PreprintCC BY-NC-ND 4.0arXiv
Uniform Computability of Isotypic Block Diagonalization for Finite-Group Representations
Abstract
We study the universal isotypic block-diagonalization problem in the Type-2 theory of effectivity (TTE). We obtain a uniform computability result for the universal block diagonalizer for commutants of given finite group representations. As an application, when the given representation is orthogonal, we compute ordinary QR factorizations blockwise in the isotypic basis. After transforming back to the original coordinates this yields a factorization A=QX, where Q is orthogonal and X is generally not upper triangular. Moreover, given a Wedderburn-adapted orthogonal basis, the transformed-back factors can be computed within the commutant.
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BibTeX
@misc{burnik2026uniform,
title = {{Uniform Computability of Isotypic Block Diagonalization for Finite-Group Representations}},
author = {Konrad Burnik},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02547},
eprint = {2610.02547},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02547},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Uniform Computability of Isotypic Block Diagonalization for Finite-Group Representations
AU - Konrad Burnik
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02547
UR - https://arxiv.org/abs/2610.02547
AB - We study the universal isotypic block-diagonalization problem in the Type-2 theory of effectivity (TTE). We obtain a uniform computability result for the universal block diagonalizer for commutants of given finite group representations. As an application, when the given representation is orthogonal, we compute ordinary QR factorizations blockwise in the isotypic basis. After transforming back to the original coordinates this yields a factorization A=QX, where Q is orthogonal and X is generally not upper triangular. Moreover, given a Wedderburn-adapted orthogonal basis, the transformed-back factors can be computed within the commutant.
ER -