论文标题
扭曲的保形块及其尺寸
Twisted conformal blocks and their dimension
论文作者
论文摘要
令$γ$成为一个有限的组，该组作用于一个简单的谎言代数$ \ mathfrak {g} $，并在$ s $上的投射曲线$（σ，\ vec {p} = \ {p_1，\ dots，p_s \}）$（for $ s $ seq 1 $）。另外，让一个合适的最高权重模块$ \ mathscr {h} _c（λ_i）$的适当扭曲的仿射谎言lie代数，由$ p_i $ in $ p_i $确定，每个$ p_i $都附加了固定的中央费用$ c $。我们证明，此数据附加的扭曲的共形块的空间是与$γ$相关的空间同构的，该$γ$由$ \ mathfrak {g} $ by tairmarg automorthismiss作用于$ \ mathfrak {g} $，并以$σ$的价格作用。在某些对分支类型的轻度条件下，我们证明，当$γ$通过图自动形态上的$ \ mathfrak {g} $作用时，可以将扭曲的共形块的维度降低到这种情况下，$ \ Mathbb {p}^1 $带有3个标记点。假设Teleman的Lie代数同源性定理具有扭曲的类似物，我们得出了Kac-Walton公式的类似物和一般$γ$ curves的Verlinde公式（对RAMIFICATION类型有轻度的限制）。特别是，如果Lie代数$ \ MATHFRAK {G} $不是类型$ d_4 $，则对RAMIFIENT类型没有限制。
Let $Γ$ be a finite group acting on a simple Lie algebra $\mathfrak{g}$ and acting on a $s$-pointed projective curve $(Σ, \vec{p}=\{p_1, \dots, p_s\})$ faithfully (for $s\geq 1$). Also, let an integrable highest weight module $\mathscr{H}_c(λ_i)$ of an appropriate twisted affine Lie algebra determined by the ramification at $p_i$ with a fixed central charge $c$ is attached to each $p_i$. We prove that the space of twisted conformal blocks attached to this data is isomorphic to the space associated to a quotient group of $Γ$ acting on $\mathfrak{g}$ by diagram automorphisms and acting on a quotient of $Σ$. Under some mild conditions on ramification types, we prove that calculating the dimension of twisted conformal blocks can be reduced to the situation when $Γ$ acts on $\mathfrak{g}$ by diagram automorphisms and covers of $\mathbb{P}^1$ with 3 marked points. Assuming a twisted analogue of Teleman's vanishing theorem of Lie algebra homology, we derive an analogue of the Kac-Walton formula and the Verlinde formula for general $Γ$-curves (with mild restrictions on ramification types). In particular, if the Lie algebra $\mathfrak{g}$ is not of type $D_4$, there are no restrictions on ramification types.
