The Brauer-Picard groups of the fusion categories coming from the $ADE$ subfactors

Understand

We compute the group of Morita auto-equivalences of the even parts of the $ADE$ subfactors, and Galois conjugates.

• To achieve this we study the braided auto-equivalences of the Drinfeld centres of these categories.
• We give planar algebra presentations for each of these Drinfeld centres, which we leverage to obtain information about the braided auto-equivalences of the corresponding categories.
• We also perform the same calculations for the fusion categories constructed from the full $ADE$ subfactors.