Spin and wedge representations of infinite-dimensional Lie algebras and groups
- 1 June 1981
- journal article
- research article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 78 (6) , 3308-3312
- https://doi.org/10.1073/pnas.78.6.3308
Abstract
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 SLn(k[t,t-1]) in spaces of sections of line bundles over infinite-dimensional homogeneous spaces (section 5).Keywords
This publication has 1 reference indexed in Scilit:
- Spinor representations of affine Lie algebrasProceedings of the National Academy of Sciences, 1980