从Jack多项式到极小模型谱
From Jack polynomials to minimal model spectra
摘要：
本文揭示了共形场论的自由场实现与对称多项式之间的深刻联系。我们简要介绍了自由场实现和对称多项式，特别是杰克对称多项式的必要条件。然后，我们结合这两个领域的分类的极小模型顶点算子代数的不可约表示作为这些方法的权力的一个启发性的例子。虽然这些结果的表示理论的极小模型都是已知的，这说明利用杰克多项式的全部权力，提出显着简化的原始证明文献。
英文摘要：
In this note, a deep connection between free field realisations of conformal field theories and symmetric polynomials is presented. We give a brief introduction into the necessary prerequisites of both free field realisations and symmetric polynomials, in particular Jack symmetric polynomials. Then we combine these two fields to classify the irreducible representations of the minimal model vertex operator algebras as an illuminating example of the power of these methods. While these results on the representation theory of the minimal models are all known, this note exploits the full power of Jack polynomials to present significant simplifications of the original proofs in the literature.
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