Year: 2026
Type: preprint
Abstract: This paper explores the algebraic invariants and ergodic behavior of the finite-index inclusions forming commuting squares of $\text{II}_1$ 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.
Source: arXiv (Cornell University)
Authors: Bakshi, Keshab Chandra, Silambarasan, C.
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204195837
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