Abstract
We determine the minimal number of separating invariants for the invariant ring of a matrix group G≤GLn(Fq) over the finite field Fq. We show that this minimal number can be obtained with invariants of degree at most |G|n(q−1). In the non-modular case this construction can be improved to give invariants of degree at most n(q−1). As examples we study separating invariants over the field F2 for two important representations of the symmetric group.
Original language | English |
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Article number | 106904 |
Journal | Journal of Pure and Applied Algebra |
Volume | 226 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2022 |
Keywords
- Generators
- Invariant theory
- Multisymmetric polynomials
- Positive characteristic
- Relations
- Separating invariants
- Symmetric group