Naoki Genra

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math.RT2025

Reduction by stages for affine W-algebras

Naoki Genra, Thibault Juillard

Given a pair of nilpotent orbits in a simple Lie algebra, one can associate a pair of vertex algebras called affine W-algebras. Under some compatibility conditions on these orbits,…

math.RT2024

Ordinary modules for vertex algebras of $osp_{1∣2 n}$

Thomas Creutzig, Naoki Genra, Andrew Linshaw

We show that the affine vertex superalgebra $V^{k} (osp_{1∣2 n})$ at generic level $k$ embeds in the equivariant $W$ -algebra of $sp_{2 n}$ times $4 n$ free…

math.RT2024

Twisted Zhu algebras

Naoki Genra

Let $V$ be a freely generated pregraded vertex superalgebra, $H$ a Hamiltonian operator of $V$ , and $g$ a diagonalizable automorphism of V commuting with $H$ with modulus $1$ eigen…

math.RT2024

Reduction by stages for finite W-algebras

Naoki Genra, Thibault Juillard

Let $g$ be a simple Lie algebra: its dual space $g^{*}$ is a Poisson variety. It is well known that for each nilpotent element $f$ in $g$ , it is poss…

Reduction by stages for affine W-algebras

Ordinary modules for vertex algebras of osp1∣2n​

Twisted Zhu algebras

Reduction by stages for finite W-algebras

Ordinary modules for vertex algebras of $osp_{1∣2 n}$