We introduce the notion of modular symmetry classes of tensors and give a necessary and sufficient condition for a modular symmetry class of tensors associated with the full symmetric group to be non-zero. Then we use modular symmetry classes of tensors to study the polynomial representations of $GL(V)$, where $V$ is a vector space over a field of characterisitic $p$. At the end we introduce a non-degenerate bilinear form on a modular symmetry class. Some problems are also given.
SHAHRYARI, M. and SHAHABI, M. A. (1999) "Modular Symmetry Classes of Tensors," Turkish Journal of Mathematics: Vol. 23: No. 3, Article 7. Available at: https://journals.tubitak.gov.tr/math/vol23/iss3/7