Spin and Wedge Representations of Infinite-Dimensional Lie Algebras and Groups
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).
- Publication:
-
Proceedings of the National Academy of Science
- Pub Date:
- June 1981
- DOI:
- 10.1073/pnas.78.6.3308
- Bibcode:
- 1981PNAS...78.3308K