Rectangular W-(super)algebras and their representations

Understand

We study W-algebras obtained by quantum Hamiltonian reduction of $sl(Mn)$ associated to the $sl(2)$ embedding of rectangular type.

• The algebra can be realized as the asymptotic symmetry of higher spin gravity with $M \times M$ matrix valued fields.
• In our previous work, we examined the basic properties of the W-algebra and claimed that the algebra can be realized as the symmetry of Grassmannian-like coset even with finite central charge based on a proposal of holography.
• In this paper, we extend the analysis in the following ways.