Spin and wedge representations of infinite-dimensional Lie algebras and groups.
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).
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
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Kac
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Peterson