Modular invariant theory: Difference between revisions

Revision as of 02:29, 12 May 2012

Revision as of 02:30, 12 May 2012

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{{harvtxt|Steinberg|1987}} gave a shorter proof of Dickson's theorem.

The matrices [''e''₁, ...,''e''_''n''] are divisible by all non-zero linear forms in the variables ''X''_''i'' with coefficients in the finite field '''F'''_''q''. In particular the [[Moore determinant over a finite field|Moore determinant]] [0, 1, ..., ''n'' − 1] is a product of such linear forms, taken over 1 + ''q'' + ''q''² + ... + ''q''^{''n'' – 1} representatives of (''n–1n''  – 1)-dimensional projective space over the field. This factorization is similar to the factorization of the [[Vandermonde determinant]] into linear factors.

[[pt:Invariante modular]]