Weyl orbits and their expansions in irreducible representations for affine Kac–Moody algebras.

Weyl orbits of affine rank 2 and 3 algebras are obtained analytically, along with the depths of their weights, in terms of an integrity basis consisting of sets of compatible (or adjacent) weights, one from each fundamental orbit. The fundamental orbits and others of the same level and congruence class are then decomposed into irreducible representations (IR). Since the orbit →IR matrix is triangular, it will be easy to invert it to get orbit multiplicities and subalgebra branching rules. [ABSTRACT FROM AUTHOR]