Matrices with involution and invariant theory

DOI10.1016/0021-8693(90)90154-GzbMath0739.16018MaRDI QIDQ1814055

Allan Berele

Publication date: 25 June 1992

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

zbMATH Keywords

Schur functionsPoincaré seriessymmetric functionsinvariant theoryalgebrassymplectic involutiontranspose involutionCayley-Hamilton equationmatrices with involutionring of generic \(n\times n\) matricestrace identities of \(n\times n\) matrices

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Vector and tensor algebra, theory of invariants (15A72) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Trace rings and invariant theory (associative rings and algebras) (16R30) Semiprime p.i. rings, rings embeddable in matrices over commutative rings (16R20)

Related Items (10)

Generic \(2\times 2\) matrices with involution ⋮ Jordan algebras of a degenerate bilinear form: Specht property and their identities ⋮ Involution codimensions and trace codimensions of matrices are asymptotically equal ⋮ Asymptotics in cocharacters of simple algebras with involution. ⋮ Embeddings for the Jordan algebra of a bilinear form ⋮ On orthogonal and special orthogonal invariants of a single matrix of small order ⋮ Denominators for the Poincaré series of invariants of matrices with involution. ⋮ On the \(*\)-cocharacter sequence of \(3\times 3\) matrices ⋮ Matrix algebras with involution and standard polynomial identities in symmetric variables ⋮ Embedding theoems for superalgebras

Cites Work

• Unnamed Item
• A conjecture of Regev about the Capelli polynomial
• Invariants and the ring of generic matrices
• Homogeneous polynomial identities
• Wreath products and P.I. algebras
• A formal inverse to the Cayley-Hamilton theorem
• A Schensted-type correspondence for the symplectic group
• The invariant theory of \(n\times n\) matrices
• Integral extensions of rings satisfying a polynomial identity
• Kronecker products for compact semisimple Lie groups
• Construction of Sp-modules by tableaux
• Glxgl- representations and ∗-polynomial identities
• Group Characters and the Structure of Groups
• Modification Rules and Products of Irreducible Representations of the Unitary, Orthogonal, and Symplectic Groups
• On invariant theory under restricted groups

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