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University of Sydney Algebra Seminar

Zachary Fehily

Friday 26 April, 12-1pm, Place: Carslaw 273

Inverse reduction and free-field realisations of W-algebras

A very useful and modern tool in the study of W-algebras are inverse reductions. These are embeddings that relate W-algebras corresponding to the same Lie algebra but different nilpotent elements. The few inverse reductions that have been constructed have proven their worth in both representation-theoretic and conformal-field-theoretic applications. In this talk, I will present a consolidated approach to constructing inverse reduction embeddings amongst hook-type sl_n W-algebras using free-field realisations. This includes the principal/regular, subregular and minimal sl_n W-algebras, and the affine sl_n vertex operator algebra. I will also detail some interesting connections, future directions and open problems.