Poincaré series of semi-invariants of 2×2 matrices Original Research Article

The Poincaré series of the algebra of image-invariants of m-tuples of 2×2 matrices is presented both as a rational function and as a series of Schur functions. We show that this algebra of invariants is generated by the determinants, the mixed discriminants and the discriminants of 2×2 matrices. Consequences on invariants of three-dimensional matrices of the shape 2×2×m are discussed. For arbitrary ngreater-or-equal, slanted2, we prove an explicit functional equation for the Poincaré series of the image-invariants of m-tuples of n×n matrices.