Decomposition rules for conformal pairs associated to symmetric spaces and abelian subalgebras of $\Bbb Z\sb 2$-graded Lie algebras.

ABSTRACT:We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial interpretation of these formulas in terms of certain abelian subalgebras of simple Lie algebras. © 2006 Elsevier Inc. All rights reserved