A classification of invertible subsets of affine root systems Original Research Article

All subsets P of an irreducible affine root system R such that P and R-45 degree ruleP are closed under addition of roots are classified. It is shown that if 0: R → R′ is a bijection of root systems such that 0 and 0−1 preserve closed sets and the irreducible components of R and R′ are affine or finite with at most one irreducible component of type Ai then θ is an isomorphism of root systems.