Separating invariants over finite fields
Copyright policy )Separating invariants over finite fields
We determine the minimal number of separating invariants for the invariant ring of a matrix group $G < \mathrm{GL}_n(\mathbb{F}_q)$ over the finite field $\mathbb{F}_q$. 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 $\mathbb{F}_2$ for two important representations of the symmetric group
18 pages
- State University of Campinas Brazil
- TECHNISCHE UNIVERSITAET MUENCHEN Germany
- Technical University of Munich Germany
13A50, 16R30, 20B30, Symmetric groups, Trace rings and invariant theory (associative rings and algebras), positive characteristic, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), invariant theory, relations, symmetric group, separating invariants, FOS: Mathematics, multisymmetric polynomials, Representation Theory (math.RT), generators, Mathematics - Representation Theory, Actions of groups on commutative rings; invariant theory
13A50, 16R30, 20B30, Symmetric groups, Trace rings and invariant theory (associative rings and algebras), positive characteristic, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), invariant theory, relations, symmetric group, separating invariants, FOS: Mathematics, multisymmetric polynomials, Representation Theory (math.RT), generators, Mathematics - Representation Theory, Actions of groups on commutative rings; invariant theory
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