Hilbert级数的最高权生成函数
Highest Weight Generating Functions for Hilbert Series
摘要：
我们发展了一种新的方法来表示希尔伯特级数的基础上的最高权Dynkin标签的对称群。该方法利用体积函数和特征生成函数以及Weyl积分。我们给出明确的例子表明如何使用这样的最高权生成函数（HWG）允许一个有效的编码和分析的希尔伯特系列的真空模空间的经典和例外的SQCD理论和模空间的瞬子。我们确定如何HWG规范不变算子的经典和特殊的SQCD理论的选择结果下对称的产品组和不变张量的规范组之间的相互作用。为了计算HWG，我们推导和制表字符生成函数的低秩组的各种方法，包括一个一般的字符生成函数，基于Weyl字符公式，为任何经典或特殊的组。
英文摘要：
We develop a new method for representing Hilbert series based on the highest weight Dynkin labels of their underlying symmetry groups. The method draws on plethystic functions and character generating functions along with Weyl integration. We give explicit examples showing how the use of such highest weight generating functions (HWGs) permits an efficient encoding and analysis of the Hilbert series of the vacuum moduli spaces of classical and exceptional SQCD theories and also of the moduli spaces of instantons. We identify how the HWGs of gauge invariant operators of a selection of classical and exceptional SQCD theories result from the interaction under symmetrisation between a product group and the invariant tensors of its gauge group. In order to calculate HWGs, we derive and tabulate character generating functions for low rank groups by a variety of methods, including a general character generating function, based on the Weyl Character Formula, for any classical or exceptional group.
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