INONU-WIGNER CONTRACTION OF KAC-MOODY ALGEBRAS

Inonu-Wigner contractions of affine Kac-Moody algebras are discussed here. The Sugawara construction for the contracted affine algebra exists only for a fixed value of the level k, which is determined in terms of the dimension of the uncontracted part of the starting Lie algebra, and the quadratic Casimir in the adjoint representation. Further, contractions of the G/H coset spaces are discussed, and an affine translation algebra is obtained, which yields a Virasoro algebra [via a Goddard-Kent-Olive (GKO) construction] with a central charge given by dim(G/H).