论文标题
$ a_ {2l}^{（2）} $在级别$ -l- \ frac {1} {2} $
$A_{2l}^{(2)}$ at level $-l-\frac{1}{2}$
论文作者
论文摘要
令$ l_ {l} = l（\ mathfrak {sl} _ {2l+1}， - l- \ frac {1} {2} {2}）$是基于offine lie algebra lie代数$ \ wideHat { $ -L- \ frac {1} {2} $。我们考虑了$ a_ {2l} = \ mathfrak {sl} _ {2l+1} $的dynkin图的相关的升力$ν$。 $ν$ -Twisted $ l_l $ -Modules是$ a_ {2l}^{（2）} $ - 级别$ -l- \ frac {1} {1} {2} $的模块，并具有反同质性实现。我们使用扭曲的Zhu代数和奇异向量对简单的$ν$ -TWIST进行了最高权重（弱）$ l_l $ - 模块，用于$ \ wideHat {\ Mathfrak {\ Mathfrak {sl}} _ {2l+1} $ at Level $ -l- \ frac {2l+1} $ at Level $ -l- \ frac {1} $ per per per per per per per per。我们发现，有一个有限的模块，直到同构，而$ν$ -twisted（feal）$ l_l $ -modules in类别$ \ mathscr {o} $ for $ a_ {2l}^{2l}^{（2）} $是半含量的。
Let $L_{l}=L(\mathfrak{sl}_{2l+1},-l-\frac{1}{2})$ be the simple vertex operator algebra based on the affine Lie algebra $\widehat{\mathfrak{sl}}_{2l+1}$ at boundary admissible level $-l-\frac{1}{2}$. We consider a lift $ν$ of the Dynkin diagram involution of $A_{2l}=\mathfrak{sl}_{2l+1}$ to an involution of $L_{l}$. The $ν$-twisted $L_l$-modules are $A_{2l}^{(2)}$-modules of level $-l-\frac{1}{2}$ with an anti-homogeneous realization. We classify simple $ν$-twisted highest-weight (weak) $L_l$-modules using twisted Zhu algebras and singular vectors for $\widehat{\mathfrak{sl}}_{2l+1}$ at level $-l-\frac{1}{2}$ obtained by Perše. We find that there are finitely many such modules up to isomorphism, and the $ν$-twisted (weak) $L_l$-modules that are in category $\mathscr{O}$ for $A_{2l}^{(2)}$ are semi-simple.
