Representation theory of infinite-dimensional Lie superalgebras and related algebraic structures

本论文的主要内容包括：（1）超共形代数的量子Hamilton约化与表示理论。(2)仿射超代数与椭圆函数的容许表示。(3)非线性李共形超代数。(4)有限单李共形超代数和李伪代数的表示论。(5)线性紧李超代数的表示理论与电弱相互作用和强相互作用模型。(6)无限维本原李超代数的分类。这项研究的动机在很大程度上是由理论物理学最近和不那么最近的发展，如标准模型和共形场论。它涉及到超对称理论的几个方向。几个长期存在的开放问题，从共形场论已经和正在解决使用量子化的经典哈密顿约化。统一的概念是线性和非线性李共形超代数的新概念，这些概念正在受到深入研究。

The proposal is concentrated around six interrelated topics: (1) Quantum Hamiltonian reduction and representation theory of superconformal algebras. (2) Admissible representations of affine superalgebras and elliptic functions.(3) Non-linear Lie conformal superalgebras. (4) Representation theory of finite simple Lie conformal superalgebras and Lie pseudoalgebras.(5) Representation theory of linearly compact Lie superalgebras and the models of electroweak and strong interactions. (6) Classification of infinite-dimensional primitive Lie superalgebras. This research is motivated to a large degree by recent and not so recent developments in Theoretical Physics, such as the Standard Model and the Conformal field theory. It is concerned with several directions of the supersymmetry theory. Several longstanding open problems from Conformal field theory have been and are being solved using the quantization of the classical Hamiltonian reduction. The unifying notion is the new notions of linear and non-linear Lie conformal superalgebras, which are being under intensive investigation.