Spinorial representations of lie groups

Abstract

We solve the question which finite dimensional irreducible orthogonal representationsof connected reductive complex Lie groups lift to the spin group We have found a criterion in terms of the highest weight of the representation essentially a polynomial in the highest weight whose value is even if and onlyif the corresponding representation lifts The criterion is closely related tothe Dynkin Index of the representation We deduce that the highest weightsof the lifting representations are periodic with a finite fundamental domain Further we calculate these periods explicitly for a few low rank groups newline newline