Rationality of the Exceptional $\mathcal {W}$-Algebras $\mathcal {W}_k(\mathfrak {sp}_{4},f_{subreg})$ Associated with Subregular Nilpotent Elements of $\mathfrak {sp}_{4}$

Justine Fasquel (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We prove the rationality of the exceptional $\mathcal {W}$-algebras $\mathcal {W}_k(\mathfrak {g},f)$ associated with the simple Lie algebra $\mathfrak {g}=\mathfrak {sp}_{4}$ and a subregular nilpotent element $f=f_{subreg}$ of $\mathfrak {sp}_{4}$, proving a new particular case of a conjecture of Kac–Wakimoto. Moreover, we describe the simple $\mathcal {W}_k(\mathfrak {g},f)$-modules and compute their characters. We also work out the nontrivial action of the component group on the set of simple $\mathcal {W}_k(\mathfrak {g},f)$-modules.

Domaines: Physique mathématique [math-ph]

Justine Fasquel. Rationality of the Exceptional $\mathcal {W}$-Algebras $\mathcal {W}_k(\mathfrak {sp}_{4},f_{subreg})$ Associated with Subregular Nilpotent Elements of $\mathfrak {sp}_{4}$. Commun.Math.Phys., 2022, 390 (1), pp.33-65. ⟨10.1007/s00220-021-04294-6⟩. ⟨hal-02959528⟩