Lie algebra automorphisms, the Weyl group, and tables of shift vectors

Abstract

The canonical lift of the Weyl group in the automorphism group of a simple Lie algebra is discussed. A constructive algorithm is given to compute the shift vector for every Weyl group conjugacy class, and tables for the simply laced Lie algebras of rank ≤ 8 are provided. Applications in physics, such as the equivalence of certain orbifold and twisted WZW string models, as well as the implication for the moduli space of 2-D conformal field theories are discussed. Show more