论文标题
广义的theta函数，投影上扁平的矢量束和非交通性托里
Generalized theta functions, projectively flat vector bundles and noncommutative tori
论文作者
论文摘要
在本文中，通过合并复杂的代数和非合理的几何形状，恢复了Theta功能与Heisenberg小组的行动之间的众所周知的关系：本质上，我们描述了赫米尔米尼 - 因斯坦 - Einstein矢量在2-tori上通过非交换托里的代表，从而使fmsushima的设置均被纳入fmsush formn forie formn fornep formn。 透明的。我们证明了在2-tori上保存自然拉普拉斯操作员的特征植物上的Hermitian-Einstein Vector束的平滑段空间上存在非交通性的圆环作用。通过对theta函数的连贯状态变换方法的激励，我们将后者扩展到矢量估值的thetas，并对Matsushima的理论进行了额外的代数重新解释，从而再次表现出FMN二元性。
In this paper, the well known relationship between theta functions and Heisenberg group actions thereon is resumed by merging complex algebraic and noncommutative geometry: in essence, we describe Hermitian-Einstein vector bundles on 2-tori via representations of noncommutative tori, thereby reconstructing Matsushima's setup and making the ensuing Fourier-Mukai-Nahm (FMN) aspects transparent. We prove the existence of noncommutative torus actions on the space of smooth sections of Hermitian-Einstein vector bundles on 2-tori preserving the eigenspaces of a natural Laplace operator. Motivated by the Coherent State Transform approach to theta functions, we extend the latter to vector valued thetas and develop an additional algebraic reinterpretation of Matsushima's theory making FMN-duality manifest again.
