Structural and Dynamical Properties of Subfactor Commuting Squares
Abstract
This paper explores the algebraic invariants and ergodic behavior of the finite-index inclusions forming commuting squares of II1 factors. We begin by establishing how regularity, intermediate-subfactor lattices, and Weyl groups transfer across the commuting square under relative commutant and irreducibility conditions. Furthermore, we provide a complete characterization, via a novel factorization theorem, of the unitary normalizers of the upper inclusion when the lower inclusion is regular. Applying these findings to crossed-product inclusions induced by discrete groups, we introduce a relative eigenbasis property that preserves regular inclusions. Finally, we contrast this by proving that a relative weak mixing condition on the group action forces the crossed-product inclusion to be singular.
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BibTeX
@misc{bakshi2026structural,
title = {{Structural and Dynamical Properties of Subfactor Commuting Squares}},
author = {Keshab Chandra Bakshi and C. Silambarasan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.23125},
eprint = {2608.23125},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.23125},
}
RIS
TY - UNPB
TI - Structural and Dynamical Properties of Subfactor Commuting Squares
AU - Keshab Chandra Bakshi
AU - C. Silambarasan
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2608.23125
UR - https://arxiv.org/abs/2608.23125
AB - This paper explores the algebraic invariants and ergodic behavior of the finite-index inclusions forming commuting squares of II_1 factors. We begin by establishing how regularity, intermediate-subfactor lattices, and Weyl groups transfer across the commuting square under relative commutant and irreducibility conditions. Furthermore, we provide a complete characterization, via a novel factorization theorem, of the unitary normalizers of the upper inclusion when the lower inclusion is regular. Applying these findings to crossed-product inclusions induced by discrete groups, we introduce a relative eigenbasis property that preserves regular inclusions. Finally, we contrast this by proving that a relative weak mixing condition on the group action forces the crossed-product inclusion to be singular.
ER -