D_l型李代数的Fock表示

Fock representation of the type D_l Lie algebras

Wakimoto自由场表示理论在A型李代数及李超代数,以及量子群上已有部分实现,但对其他型了解得并不多,本文将类似的想法实现于D型李代数上.分析了D型李代数根系的结构特点,构造出Dl型李代数的一类Fock表示,并给出l=4时这类表示不可约时参数的条件.进一步完成了这类表示在非扭D型仿射Kac-Moody李代数上的实现,不同于半单的情形,这种仿射李代数的表示大部分都是不可约的.

There have been some Wakimoto free field realizations of Lie algebra,Lie super algebra,and even type A quantum group,but little is known about other types.In this paper,root structure of type D Lie algebra is analyzed,a Fock representation of type DlLie algebras is constructed,the condition of irreducibility is given.Further,the realization for the untwisted affine Kac-Moody Lie algebra was done,the irreducibility is proved.Different from semi-simple algebra,most representations of affine Lie algebra are found irreducible.