Towards logarithmic representation theory of W-algebras

目的：构造和分析保形场论中意义的不可分解表示。 意义：保形场理论在数学和物理学的许多发展中起着关键作用。对数共形场理论支配着重要的系统，如二维临界渗流。这一建议旨在发展理解由对数共形场理论描述的关键系统的显著特征所必需的表示理论。 预期结果：对数共形场理论中基本重要性的新表示。 好处：解决了对数共形场理论中的公开问题，从而延续了澳大利亚该领域的强大传统。

Aims: To construct and analyse indecomposable representations of significance in conformal field theory. Significance: Conformal field theory plays a key role in many developments in mathematics and physics. Logarithmic conformal field theories govern important systems such as two-dimensional critical percolation. This proposal aims to develop the representation theory necessary for understanding salient features of critical systems described by logarithmic conformal field theory. Expected Outcomes: Novel representations of fundamental importance in logarithmic conformal field theory. Benefit: Resolution of open problems in logarithmic conformal field theory, thus continuing the strong tradition in the field in Australia.