论文标题
拓扑理论的普遍构建二维
Universal construction of topological theories in two dimensions
论文作者
论文摘要
我们认为Blanchet，Habegger，Masbaum和Vogel在维度二中对拓扑理论的普遍构建，使用它来产生有趣的理论，这些理论无法满足通常的二维TQFT公理。克罗内克（Kronecker）对理性函数的表征使我们能够通过有限维态空间在字段上对理论进行分类，并将其扩展为n和m变量中对称函数的环的产物引入理论。我们查看了几个非培养理论的例子，并参见Hankel矩阵，Schur和超对称Schur多项式从这些结构中迅速出现。最后一部分解释了罗伯特 - 瓦格纳泡沫评估对重叠泡沫的扩展如何为Sergeev-pragacz sergeev-pragacz公式用于超对称schur多项式的多项式，以及作为特殊情况的理性功率序列决定因素的日常公式。
We consider Blanchet, Habegger, Masbaum and Vogel's universal construction of topological theories in dimension two, using it to produce interesting theories that do not satisfy the usual two-dimensional TQFT axioms. Kronecker's characterization of rational functions allows us to classify theories over a field with finite-dimensional state spaces and introduce their extension to theories with the ground ring the product of rings of symmetric functions in N and M variables. We look at several examples of non-multiplicative theories and see Hankel matrices, Schur and supersymmetric Schur polynomials quickly emerge from these structures. The last section explains how an extension of the Robert-Wagner foam evaluation to overlapping foams gives the Sergeev-Pragacz formula for the supersymmetric Schur polynomials and the Day formula for the Toeplitz determinant of rational power series as special cases.
