论文标题
通用自动形态功能的程序的草图，以捕获可怕的月光
Sketch of a Program for Universal Automorphic Functions to Capture Monstrous Moonshine
论文作者
论文摘要
我们审查并重新制定了有关三合会$ {\ rm ppsl} _2（{\ mathbb z}）\ subseteq {\ rm ppsl} _2（{\ mathbb r}）\ circlearrowirt ppsl_2（{ triad $ {\ rm psl} _2（{\ mathbb z}）\ subseteq {\ rm psl} _2（{\ mathbb r}）\ circlearlrowrowrowright psl_2（{\ mathbb r}）$。通用设置中的领先p或$ p $代表$分段$，组$ {\ rm ppsl} _2（{\ mathbb z}）$立即扮演通用模块化组，通用模块化组，汤普森组$ t $ t $ t $ and tolemy group的角色。我们产生了一个新的基础，该元代数$ ppsl_2（{\ mathbb r}）$，计算其结构常数，定义了一个中心扩展，该中心扩展与Weil-petersson 2形式进行了比较，并讨论了其表示理论。我们在通用的Teichmüller空间及其对称组$ {\ rm ppsl} _2（{\ Mathbb r}）$上构建和研究新框架全息坐标，并构建了与不变的eisenstein 1-Form $ e _2（z）的不变的1型（Z），并构建了一种不变的1形式，该cartan cartan cartan cartan cartan cartan-cartan形成了同类型。 $ psl_2（{\ Mathbb r}）$由微不足道表示。这表明了开发通用自动形态功能理论的完整程序，该理论猜想产生了玻感CFT $ _2 $。放松自身形态状况到换向物，这导致了我们通过通用三合会的自动形态表示怪物CFT $ _2 $的最终猜想。通用Teichmüller和Monster CFT $ _2 $理论与三维量子引力的链接也支持了这一猜想。
We review and reformulate old and prove new results about the triad $ {\rm PPSL}_2({\mathbb Z})\subseteq{\rm PPSL}_2({\mathbb R})\circlearrowright ppsl_2({\mathbb R}) $, which provides a universal generalization of the classical automorphic triad ${\rm PSL}_2({\mathbb Z})\subseteq{\rm PSL}_2({\mathbb R})\circlearrowright psl_2({\mathbb R})$. The leading P or $p$ in the universal setting stands for $piecewise$, and the group ${\rm PPSL}_2({\mathbb Z})$ plays at once the role of universal modular group, universal mapping class group, Thompson group $T$ and Ptolemy group. We produce a new basis of the Lie algebra $ppsl_2({\mathbb R})$, compute its structure constants, define a central extension which is compared with the Weil-Petersson 2-form, and discuss its representation theory. We construct and study new framed holographic coordinates on the universal Teichmüller space and its symmetry group ${\rm PPSL}_2({\mathbb R})$, and construct an invariant 1-form as its Maurer-Cartan form analogous to the invariant Eisenstein 1-form $E_2(z)dz$, which gives rise to the spin 1 representation of $psl_2({\mathbb R})$ extended by the trivial representation. This suggests the full program for developing the theory of universal automorphic functions conjectured to yield the bosonic CFT$_2$. Relaxing the automorphic condition to the commutant leads to our ultimate conjecture on realizing the Monster CFT$_2$ via the automorphic representation for the universal triad. This conjecture is also bolstered by the links of both the universal Teichmüller and the Monster CFT$_2$ theories to the three-dimensional quantum gravity.
