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Orthogonal bases of Brauer symmetry classes of tensors for groups having cyclic support on non-linear Brauer characters
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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.
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Title: Orthogonal bases of Brauer symmetry classes of tensors for groups having cyclic support on non-linear Brauer characters
Description:
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.
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