论文标题
与根系相关的theta块
Theta blocks related to root systems
论文作者
论文摘要
Gritsenko，Skoruppa和Zagier与root System $ r $ a theta Block $ \ vartheta_r $相关联，这是晶格索引的雅各比形式。我们对theta块$ \ vartheta_r $的$ q $ - 订单$ 1 $进行了分类，并表明他们的Gritsenko Lift是一种强烈反射的Borcherds singular Weight的产品，这与Conway的$ \ operatateRatorNAME {CO} _0 _0 $相关。作为推论，我们获得了Gritsenko的theta块猜想的证明，对于函数$ \ vartheta_r $的专业化而获得的纯theta块。
Gritsenko, Skoruppa and Zagier associated to a root system $R$ a theta block $\vartheta_R$, which is a Jacobi form of lattice index. We classify the theta blocks $\vartheta_R$ of $q$-order $1$ and show that their Gritsenko lift is a strongly-reflective Borcherds product of singular weight, which is related to Conway's group $\operatorname{Co}_0$. As a corollary we obtain a proof of the theta block conjecture by Gritsenko, Poor and Yuen for the pure theta blocks obtained as specializations of the functions $\vartheta_R$.
