A stable range for dimensions of homogeneous \(O(n)\)-invariant polynomials on the \(n\times n\) matrices

DOI10.1006/jabr.2001.8828zbMath1008.16024OpenAlexW2034402566MaRDI QIDQ5945131

Jeb F. Willenbring

Publication date: 3 November 2002

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2001.8828

zbMATH Keywords

Hilbert seriesSchur-Weyl dualitytracesLittlewood-Richardson coefficientsorthogonal invariantssymmetric pairs

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Vector and tensor algebra, theory of invariants (15A72) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Actions of groups on commutative rings; invariant theory (13A50) Trace rings and invariant theory (associative rings and algebras) (16R30)

Related Items (2)

Stable Hilbert series of \(\mathcal S(\mathfrak g)^{K}\) for classical groups ⋮ Polynomial invariants on matrices and partition, Brauer algebras

Uses Software

• SF

Cites Work

• The invariant theory of \(n\times n\) matrices
• A Maple package for symmetric functions
• Remarks on Classical Invariant Theory
• Invariant Theory
• On Some q-Analogs of a Theorem of Kostant-Rallis
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