Indecomposable orthogonal invariants of several matrices over a field of positive characteristic

We consider the algebra of invariants of $d$-tuples of $n\times n$ matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic $p$ different from two. It is well-known that this algebra is generated by the coefficients of the characteristic polynomial of all products of generic and transpose generic $n\times n$ matrices. We establish that in case $0
Comment: Version 2: some proofs are more detailed; to appear in International Journal of Algebra and Computation