Inonu-Wigner Contractions of Kac-Moody Algebras

Abstract

We discuss Inönü-Wigner contractions of affine Kac-Moody algebras. We show that 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, we discuss contractions of $G/H$ coset spaces, and obtain an affine {\it translation} algebra, which yields a Virasoro algebra (via a GKO construction) with a central charge given by $dim(G/H)$.

11 pages, IMSc/92-26

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