Minimal system of generators for O(4)-invariants of two skew-symmetric matrices

Abstract

The algebra of invariants of d-tuples of skew-symmetric matrices under the action of the orthogonal group O(n) by the simultaneous conjugation is considered over an infinite field of characteristic different from two. It is well-known that this algebra is generated by the coefficients of the characteristic polynomial of all products of generic skew-symmetric matrices. We establish a minimal generating system for the case of two skew-symmetric matrices.

Keywords:

• Invariant theory
• matrix invariants
• classical linear groups
• generators
• positive characteristic

AMS Subject Classifications:

• 16R30
• 15B10
• 13A50

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by RFBR [16-31-60111] (mol_a_dk).