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Works connected to Masaki Izumi

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M. Izumi, V. F. R. Jones, S. Morrison, and N. Snyder: “Subfactors of index less than 5, III: Quadruple points,” Comm. Math. Phys. 316 : 2 (2012), pp. 531–554. MR 2993924 Zbl 1272.46051 ArXiv 1109.3190 article

One major obstacle in extending the classification of small index subfactors beyond \( 3+\sqrt{3} \) is the appearance of infinite families of candidate principal graphs with 4-valent vertices (in particular, the “weeds” \( \mathcal{Q} \) and \( \mathcal{Q}^{\prime} \) from [Morrison and Snyder 2012]. Thus instead of using triple point obstructions to eliminate candidate graphs, we need to develop new quadruple point obstructions. In this paper we prove two quadruple point obstructions. The first uses quadratic tangles techniques and eliminates the weed \( \mathcal{Q}^{\prime} \) immediately. The second uses connections, and when combined with an additional number theoretic argument it eliminates both weeds \( \mathcal{Q} \) and \( \mathcal{Q}^{\prime} \). Finally, we prove the uniqueness (up to taking duals) of the 3311 Goodman–de la Harpe–Jones subfactor using a combination of planar algebra techniques and connections.

Noah Snyder	Related
Scott Morrison	Related
Masaki Izumi	Related