Minimal W-algebras with non-admissible levels and intermediate Lie algebras

Authors: Kaiwen Sun

Preprint number: UUITP-15/24

Abstract: In [Kawasetsu:2018irs], Kawasetsu proved that the simple W-algebra associated with a minimal nilpotent element W k(g, f_θ) is rational and C2-cofinite for g = D₄, E₆, E₇, E₈ with non-admissible level k = −h^∨/6. In this paper, we study W k(g, f_θ) algebra for g = E₆, E₇, E₈ with non-admissible level k = −h^∨/6 + 1. We determine all irreducible (Ramond twisted) modules, compute their characters and find coset constructions and Hecke operator interpretations. These W-algebras are closely related to intermediate Lie algebras and intermediate vertex subalgebras.