3-transposition groups arising in VOA theory

On 3-transposition groups generated by $σ$-involutions associated to c=4/5 Virasoro vectors

In this paper, we show that $σ$-involutions associated to extendable c=4/5 Virasoro vectors generate a 3-transposition group in the automorphism group of a vertex operator algebra (VOA). Several explicit examples related to lattice VOA are also discussed in details. In particular, we show that the automorphism group of the VOA $V_{K_{12}}^{\hatν}$ associated to the Coxeter Todd lattice $K_{12}$ contains a subgroup isomorphic to ${}^+Ω^{-}(8,3)$.

3-Transposition Groups of Symplectic Type and Vertex Operator Algebras

The 3-transposition groups that act on a vertex operator algebra in the way described by Miyamoto are classified under the assumption that the group is centerfree and the VOA carries a positive-definite invariant Hermitian form. This generalizes and refines the result of Kitazume and Miyamoto. Application to a similar but different situation is also considered in part by a slight generalization of the argument.

关于源自秩一4D SCFT的非容许水平上的若干简单轨形仿射VOA

On some simple orbifold affine VOAs at non-admissible level arising from rank one 4D SCFTs

本文研究源自秩一4D SCFT的非容许水平仿射顶点代数，分类$L_{-2}(G_2)$与$L_{-2}(B_3)$的不可约最高权模，并证明前者的伴生簇是$L_{-2}(D_4)$伴生簇在三次对称群下的轨形。

Vertex operator algebra arising from the minimal series M(3,p) and monomial basis

We study a vertex operator algebra (VOA) V related to the M(3,p) Virasoro minimal series. This VOA reduces in the simplest case p=4 to the level two integrable vacuum module of $\hat{sl}_2$. On V there is an action of a commutative current a(z), which is an analog of the current e(z) of $\hat{sl}_2$. Our main concern is the subspace W generated by this action from the highest weight vector of V. Using the Fourier components of a(z), we present a monomial basis of W and a semi-infinite monomial basis of V. We also give a Gordon type formula for their characters.

离散系列 Virasoro VOA $\text{Vir}_{2k+1,2}$ 的共形块因子

Conformal Block Divisors for Discrete Series Virasoro VOA $\text{Vir}_{2k+1,2}$

本文研究由 Virasoro VOA 表示构造的曲线模空间上的向量丛，证明其第一陈类在多数情形下为 nef，并给出亏格1时的 Q-基及非线性 nef 插值。

单位ary N=(2,2) 全顶点代数的上同调环与镜像对称

Cohomology ring of unitary $N=(2,2)$ full vertex algebra and mirror symmetry

本文研究了N=(2,2)超对称共形场论的上同调环、Hodge数及Witten指数，通过构造泛化全顶点算子超代数，探讨了上同调环的Poincaré对称、T对称及Frobenius代数结构，并讨论了镜像对称与Hodge理论的关系。