Speaker
Description
We want to discuss aspects of ODE/IM correspondence for WN algebras, with particular focus on the relevant symmetries of the family (in particular the triality symmetry) and the associated geometric structures.
We develop a systematic procedure for calculating the expressions for local higher spin charges in terms of solutions of Bethe ansatz equations of BLZ type (we write these equations explicitly for the case of W3 and W3 algebras). The key step is the application of WKB analysis to the operator associated via ODE/IM correspondence to each eigenstate of the commuting Hamiltonians.
The WKB curve is a branched covering curve of three-punctured sphere, which we identify with the mirror curve appearing in the related context of topological string (topological vertex). Due to high symmetries of the problem, all the calculations are reduced to this mirror curve.
