Brauer symmetry classes of tensors, Orthogonal basis, Semi-dihedral groups, Dicyclic groups
This paper provides some properties of Brauer symmetry classes of tensors. A dimension formula is derived for the orbital subspaces in the Brauer symmetry classes of tensors corresponding to the irreducible Brauer characters of the groups whose non-linear Brauer characters have support being a cyclic group. Using the derived formula, necessary and sufficient condition are investigated for the existence of an o-basis of dicyclic groups, semi-dihedral groups, and also those things are reinvestigated on dihedral groups. Some criteria for the non-vanishing elements in the Brauer symmetry classes of tensors associated to those groups are also included.
Hormozi, Mahdi and Rodtes, Kijti.
"Orthogonal bases of Brauer symmetry classes of tensors for groups having cyclic support on non-linear Brauer characters",
Electronic Journal of Linear Algebra,
Volume 31, pp. 263-285.