Computing with rational symmetric functions and applications to invariant theory and PI-algebras

zbMath1374.13009arXiv1201.4448MaRDI QIDQ2963542

Plamen Koev, Silvia Boumova, Georgi K. Genov, Francesca Saviella Benanti, Vesselin Drensky

Publication date: 14 February 2017

Full work available at URL: https://arxiv.org/abs/1201.4448

zbMATH Keywords

Hilbert seriesclassical invariant theoryalgebras with polynomial identitynoncommutative invariant theorycocharacter sequenceMacMahon partition analysisRational symmetric functions

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Representation theory for linear algebraic groups (20G05) Vector and tensor algebra, theory of invariants (15A72) Actions of groups on commutative rings; invariant theory (13A50) Trace rings and invariant theory (associative rings and algebras) (16R30) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

Related Items (10)

Graded algebras, algebraic functions, planar trees, and elliptic integrals ⋮ Invariants of symplectic and orthogonal groups acting on $GL(n,CC)$-modules ⋮ Invariant theory of free bicommutative algebras ⋮ Weitzenböck derivations of free metabelian Lie algebras ⋮ Hermitian matrices with a bounded number of eigenvalues ⋮ On the \(\mathrm{GL}(n)\)-module structure of Lie nilpotent associative relatively free algebras ⋮ Weitzenböck derivations of free metabelian associative algebras ⋮ Noncommutative invariant theory of symplectic and orthogonal groups ⋮ Classical invariant theory for free metabelian Lie algebras ⋮ Multigraded Hilbert series of noncommutative modules

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