The Hilbert series of rings of matrix concomitants

DOI10.1017/S0027763000001057zbMath0675.16010MaRDI QIDQ3829680

Yasuo Teranishi

Publication date: 1988

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

functional equationring of invariantsfree modulesHilbert seriescentregeneric n\(\times n\) matricestrace ringring of polynomial concomitants

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Representation theory for linear algebraic groups (20G05) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Vector and tensor algebra, theory of invariants (15A72) Graded rings and modules (associative rings and algebras) (16W50) Representations of infinite symmetric groups (20C32) Rings with polynomial identity (16Rxx)

Related Items (11)

Rings of invariants of \(2\times 2\) matrices in positive characteristic ⋮ Universal induced characters and restriction rules for the classical groups ⋮ Poincaré series of some pure and mixed trace algebras of two generic matrices. ⋮ Algebraic independence in \(\mathrm{SL}(3, \mathbb C)\) character varieties of free groups ⋮ Denominators for one variable Poincaré series of generic matrices ⋮ Rank 1 character varieties of finitely presented groups ⋮ Minimal affine coordinates for SL\((3,\mathbb C)\) character varieties of free groups ⋮ Orthogonal invariants of skew-symmetric matrices ⋮ Explicit descriptions of trace rings of generic 2 by 2 matrices ⋮ Separating invariants for \(2 \times 2\) matrices ⋮ Rings of matrix invariants in positive characteristic

Cites Work

• Computing with 2\(\times 2\) matrices
• Invariants and the ring of generic matrices
• The Poincaré series of the ring of 2x2 generic matrices
• The invariant theory of \(n\times n\) matrices
• Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay
• The ring of invariants of matrices

This page was built for publication: The Hilbert series of rings of matrix concomitants