标题： 任意子、para玻色子和so(\infty )与osp(1|\infty )的表示 显示英文标题

标题： Parafermions, parabosons and representations of so(\infty) and osp(1|\infty)

摘要： 本文的目标是为parafermion和paraboson代数的Fock空间给出一个显式的构造方法，其中生成元集是无限的。 这等价于构建某些（无限秩）Lie代数so(\infty )和Lie超代数osp(1|\infty )的特定酉不可约最低权表示。 问题的一个完整解被提出，其中Fock空间具有由某些无限但稳定的Gelfand-Zetlin模式标记的基本向量，并且明确给出了基变换。 我们还给出了Fock空间表示的特征表达式。 显示英文摘要

摘要： The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations of the (infinite rank) Lie algebra so(\infty) and of the Lie superalgebra osp(1|\infty). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labelled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation of the basis is given explicitly. We also present expressions for the character of the Fock space representations.