  Geometric complexity theory (GCT) is an approach towards separating algebraic
complexity classes through algebraic geometry and representation theory.
Originally Mulmuley and Sohoni proposed (SIAM J Comput 2001, 2008) to use
occurrence obstructions to prove Valiant's determinant vs permanent conjecture,
but recently B\"urgisser, Ikenmeyer, and Panova (Journal of the AMS 2019)
proved this impossible. However, fundamental theorems of algebraic geometry and
representation theory grant that every lower bound in GCT can be proved by the
use of so-called highest weight vectors (HWVs). In the setting of interest in
GCT (namely in the setting of polynomials) we prove the NP-hardness of the
evaluation of HWVs in general, and we give efficient algorithms if the
treewidth of the corresponding Young-diagram is small, where the point of
evaluation is concisely encoded as a noncommutative algebraic branching
program! In particular, this gives a large new class of separating functions
that can be efficiently evaluated at points with low (border) Waring rank.
