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Jingtian Song

Publications and source records attributed to Jingtian Song.

2 recordsLinked to original sources

arXiv2025

On singular vectors of simply-laced universal affine vertex operator algebras

Given a finite-dimensional complex simple Lie algebra $\mathfrak{g}$ and a complex number $\kappa$, let $V^{\kappa}(\mathfrak{g})$ be the associated universal affine vertex algebra. Gorelik and Kac [GK07] gave a sufficient and necessary condition for $V^{\kappa}(\mathfrak{g})$ to be simple. In this paper, for simply-laced $\mathfrak{g}$ and non-critical $\kappa$, we determine the weights of singular vectors of $V^{\kappa}(\mathfrak{g})$ with minimal conformal weights, when $V^{\kappa}(\mathfrak{g})$ is not simple. We further determine all the longest Weyl elements in the Kashiwara-Tanisaki character theorem [KT00] which correspond to the weights of the singular vectors.

math.QA↗

arXiv2025

Associated varieties of simple affine VOAs $L_k(sl_3)$ and $W$-algebras $W_k(sl_3,f)$

In this paper we first prove that the maximal ideal of the universal affine vertex operator algebra $V^k(sl_n)$ for $k=-n+\frac{n-1}{q}$ is generated by two singular vectors of conformal weight $3q$ if $n=3$, and by one singular vector of conformal weight $2q$ if $n\geq 4$. We next determine the associated varieties of the simple vertex operator algebras $L_k(sl_3)$ for all the non-admissible levels $k=-3+\frac{2}{2m+1}$, $m\geq 0$. The varieties of the associated simple affine $W$-algebras $W_k(sl_3,f)$, for nilpotent elements $f$ of $sl_3$, are also determined.

math.QA↗