Spin and wedge representations of infinite-dimensional Lie algebras and groups.
Spin and wedge representations of infinite-dimensional Lie algebras and groups.
复制标题
DOI：
10.1073/pnas.78.6.3308
复制
发表时间：
1981-06
影响因子：
11.1
通讯作者：
V. Kac;D. Peterson
中科院分区：
文献类型：
--
作者：
V. Kac;D. Peterson
我们提出了一个无限维正交李代数的自旋表示的纯代数构造（第1节和第2节）和一个相应的群（第4节）。由此，我们推导出了在无限维Grassmann代数上，正交仿射李代数的所有第一级最高权表示的生成和湮灭算子的构造（第3节）。我们还给出了无限维“楔形空间”中一般线性仿射李代数的一级表示的类似构造。“沿着这些线，我们构造了群SL（n）（k[t，t（-1）]）在无限维齐性空间上的线丛的截面空间中的泛中心扩张的相应表示（第5节）。
We suggest a purely algebraic construction of the spin representation of an infinite-dimensional orthogonal Lie algebra (sections 1 and 2) and a corresponding group (section 4). From this we deduce a construction of all level-one highest-weight representations of orthogonal affine Lie algebras in terms of creation and annihilation operators on an infinite-dimensional Grassmann algebra (section 3). We also give a similar construction of the level-one representations of the general linear affine Lie algebra in an infinite-dimensional "wedge space." Along these lines we construct the corresponding representations of the universal central extension of the group SL(n)(k[t,t(-1)]) in spaces of sections of line bundles over infinite-dimensional homogeneous spaces (section 5).