We give a lower bound for the Waring rank and cactus rank of forms that are invariant under an action of a connected algebraic group. We use this to improve the Ranestad-Schreyer-Shafiei lower bounds for the Waring ranks and cactus ranks of determinants of generic matrices, Pfaffians of generic skew-symmetric matrices, and determinants of generic symmetric matrices.
This is an author-produced, peer-reviewed version of this article. © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-No Derivatives 4.0 License. Details regarding the use of this work can be found at: http://creativecommons.org/licenses/by-nc-nd/4.0/ . The final, definitive version of this document can be found online at Journal of Pure and Applied Algebra, doi 10.1016/j.jpaa.2015.05.025
Derksen, Harm and Teitler, Zach. (2015). "Lower Bound for Ranks of Invariant Forms". Journal of Pure and Applied Algebra, 219(12), 5429-5441.