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- W4300663248 abstract "We work over a field K of characteristic zero. The Poincare series for the algebra C_{n,2} of GL_n-invariants and the algebra T_{n,2} of GL_n-concomitants of two generic n x n matrices x and y are presented for n less than or equal 6. Both simply graded and bigraded cases are included. The cases for n at most 4 were known previously. If n=5 or 6, we show that C_{n,2} has no bigraded system of parameters. For the algebra C_{4,2} and C_{5,2} we construct a minimal set of generators and give an application to Specht's theorem on unitary similarity of two complex matrices. Five conjectures are proposed concerning the numerators and denominators of various Poincare series mentioned above. Some heuristic formulas and open problems are stated." @default.
- W4300663248 created "2022-10-03" @default.
- W4300663248 creator A5035614623 @default.
- W4300663248 date "2006-09-09" @default.
- W4300663248 modified "2023-09-28" @default.
- W4300663248 title "Poincare series of some pure and mixed trace algebras of two generic matrices" @default.
- W4300663248 doi "https://doi.org/10.48550/arxiv.math/0609262" @default.
- W4300663248 hasPublicationYear "2006" @default.
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