论文标题
组合拓扑理论和群体理论算法
Combinatoric topological string theories and group theory algorithms
论文作者
论文摘要
最近已证明，基于Dijkgraaf-witten在表面上平坦的G-Bundles的dijkgraaf-witten理论的组合式拓扑字符串（G-CTST）构建有限组中构造表示形式数据的代表理论数据的有限算法。我们使用Twisted Dijkgraaf-Witten理论将此结果扩展到G的投影表示。根据手柄创建操作员和最小的乘法生成子空间的介绍，描述了字符的新算法。这种最小的生成子空间与ADS/CFT对应的信息理论方面有关。对于未透视的情况，我们描述了从这些建设性的G-CTST算法中遵循的某些字符总和和字符幂和总和的完整性属性。这些整数总和显示为G-CTST生成函数中的奇异性残基。组合拓扑字符串的S偶性激发了代数代数和扭曲组代数中心的逆处理创建操作员的定义。
A number of finite algorithms for constructing representation theoretic data from group multiplications in a finite group G have recently been shown to be related to amplitudes for combinatoric topological strings (G-CTST) based on Dijkgraaf-Witten theory of flat G-bundles on surfaces. We extend this result to projective representations of G using twisted Dijkgraaf-Witten theory. New algorithms for characters are described, based on handle creation operators and minimal multiplicative generating subspaces for the centers of group algebras and twisted group algebras. Such minimal generating subspaces are of interest in connection with information theoretic aspects of the AdS/CFT correspondence. For the untwisted case, we describe the integrality properties of certain character sums and character power sums which follow from these constructive G-CTST algorithms. These integer sums appear as residues of singularities in G-CTST generating functions. S-duality of the combinatoric topological strings motivates the definition of an inverse handle creation operator in the centers of group algebras and twisted group algebras.
