论文标题
在计数张量模型中，可观察到$ u（n）$和$ o（n）$ classical不变性
On the counting tensor model observables as $U(N)$ and $O(N)$ classical invariants
论文作者
论文摘要
真实或复杂的张量模型可观察物，张量理论空间的骨干是经典的（单一，正交，符号单位）谎言组不变性。这些可观察的物品表示为彩色图，并且该表示形式提供了研究其组合，拓扑和代数特性的手柄。我们在这里概述了对称群体的理论表述，该列表的单一和正交不变的可观察结果证明了这一结构丰富的结构。从他们的计数公式中，人们找到了与2细胞复合物上拓扑场理论的对应关系，从而带来了对同一计数的其他解释。此外，张量模型可观察物跨越了一个代数，该代数被证明是半简单的。在处理复杂的张量时，我们讨论了代数的代表理论基础，使其明确的Wedderburn-Artin分解。作为其Wedderburn-Artin分解的基础，实际情况更加微妙。
Real or complex tensor model observables, the backbone of the tensor theory space, are classical (unitary, orthogonal, symplectic) Lie group invariants. These observables represent as colored graphs, and that representation gives an handle to study their combinatorial, topological and algebraic properties. We give here an overview of the symmetric group-theoretic formulation of the enumeration of unitary and orthogonal invariant observables which turns out to bear a rich structure. From their counting formulae, one finds a correspondence with topological field theory on 2-cellular complexes that brings other interpretations of the same countings. Furthermore, tensor model observables span an algebra that turns out to be semi-simple. Dealing with complex tensors, we discuss the representation theoretic base of the algebra making explicit its Wedderburn-Artin decomposition. The real case is more subtle as a base of its Wedderburn-Artin decomposition is yet unknown.
