On the structure of W-algebras in type A - Creutzig, Thomas; Fasquel, Justine; Linshaw, Andrew R.; Nakatsuka, Shigenori (Japanese Journal of Mathematics, 2025)
We formulate and prove examples of a conjecture which describes the W−algebras in type A as successive quantum Hamiltonian reductions of affine vertex algebras associated with several hook-type nilpotent orbits. This implies that the affine coset subalgebras of hook-type W−algebras are building blocks of the W−algebras in type A. In the rational case, it turns out that the building blocks for the simple quotients are provided by the minimal series of the regular W−algebras. In contrast, they are provided by singlet-type extensions of W−algebras at collapsing levels which are irrational. In the latter case, several new sporadic isomorphisms between different W−algebras are established.
CRIS-Team Scopus Importer:2025-04-01
Keywords: affine W-algebras; collapsing levels; inverse Hamiltonian reductions; reductions by stage; universal W-algebras