Spin representations of real reflection groups of noncrystallographic root systems

Abstract

A uniform parametrization for the irreducible spin representations of Weyl groups in terms of nilpotent orbits is recently achieved by Ciubotaru (2011). This paper is a generalization of this result to other real reflection groups.Let (V0,R,V0∨,R∨) be a root system with the real reflection group W. We define a special subset of points in V0∨ which will be called solvable points. Those solvable points, in the case R crystallographic, correspond to the nilpotent orbits whose elements have a solvable centralizer in the corresponding Lie algebra. Then a connection between the irreducible spin representations of W and those solvable points in V0∨ is established. © 2013 Elsevier Inc.