Search results for "Cocharacter Sequence"

showing 2 items of 2 documents

Computing with Rational Symmetric Functions and Applications to Invariant Theory and PI-algebras

2012

The research of the first named author was partially supported by INdAM. The research of the second, third, and fourth named authors was partially supported by Grant for Bilateral Scientific Cooperation between Bulgaria and Ukraine. The research of the fifth named author was partially supported by NSF Grant DMS-1016086.

Classical Invariant Theory05A15 05E05 05E10 13A50 15A72 16R10 16R30 20G05MacMahon Partition AnalysisHilbert SeriesRational symmetric functions classical invariant theory algebras with polynomial identity cocharacter sequenceMathematics - Rings and AlgebrasCommutative Algebra (math.AC)Mathematics - Commutative AlgebraRational Symmetric FunctionsAlgebras with Polynomial IdentitySettore MAT/02 - AlgebraRings and Algebras (math.RA)Noncommutative Invariant TheoryFOS: MathematicsCocharacter SequenceMathematics - CombinatoricsCombinatorics (math.CO)
researchProduct

On the ∗-cocharacter sequence of 3×3 matrices

2000

Abstract Let M 3 (F) be the algebra of 3×3 matrices with involution * over a field F of characteristic zero. We study the ∗ -polynomial identities of M 3 (F) , where ∗=t is the transpose involution, through the representation theory of the hyperoctahedral group B n . After decomposing the space of multilinear ∗ -polynomial identities of degree n under the B n -action, we determine which irreducible B n -modules appear with non-zero multiplicity. In symbols, we write the nth ∗ -cocharacter χ n (M 3 (F),*)=∑ r=0 n ∑ λ⊢r,h(λ)⩽6 μ⊢n−r,h(μ)⩽3 m λ,μ χ λ,μ , where λ and μ are partitions of r and n−r , respectively, χ λ,μ is the irreducible B n -character associated to the pair (λ,μ) and m λ,μ ⩾0 i…

Discrete mathematicsNumerical AnalysisMultilinear mapAlgebra and Number TheoryMultiplicity (mathematics)Hyperoctahedral groupRepresentation theoryPolynomial identitiesCombinatoricsMatrices with involutionCocharacter sequenceDiscrete Mathematics and CombinatoricsGeometry and TopologyMathematicsLinear Algebra and its Applications
researchProduct