Spin and wedge representations of infinite-dimensional Lie algebras and groups

AUTOR(ES)

Kac, Victor G.

RESUMO

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).

Documentos Relacionados

• Modular invariant representations of infinite-dimensional Lie algebras and superalgebras
• Laplace operators of infinite-dimensional Lie algebras and theta functions
• Isotropic probability measures in infinite-dimensional spaces
• Isotropic probability measures in infinite-dimensional spaces
• Dedekind's η-function and the cohomology of infinite dimensional Lie algebras