On the decomposition of Brauer's centralizer algebras

DOI10.1016/0021-8693(89)90076-8zbMath0695.20026OpenAlexW1982697846MaRDI QIDQ909795

David B. Wales, Philip J. Hanlon

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0021-8693(89)90076-8

zbMATH Keywords

symplectic grouporthogonal groupeigenvaluessymmetric matrixrepresentations of symmetric groupsradicalrepresentations of algebraic groupssimple componentscentralizing algebra of tensor space

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05)

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Schur–Weyl Dualities Old and New ⋮ The homology of the Brauer algebras ⋮ Commutators of random matrices from the unitary and orthogonal groups ⋮ On the semi-simplicity of the cyclotomic Brauer algebras. ⋮ Tensor Product Representations of the Lie Superalgebra 𝔭(n) and Their Centralizers ⋮ On partition functions for 3-graphs ⋮ Young modules and filtration multiplicities for Brauer algebras. ⋮ The tautological ring of \(M_{1,n}^{ct}\) ⋮ Graph parameters from symplectic group invariants ⋮ Polynomial representations, algebraic monoids, and Schur algebras of classical type ⋮ Alcove geometry and a translation principle for the Brauer algebra. ⋮ On the existence of real R-matrices for virtual link invariants ⋮ Partition functions from orthogonal and symplectic group invariants ⋮ Gromov–Witten theory of complete intersections via nodal invariants ⋮ Identities in twisted Brauer monoids ⋮ Eigenvalues connected with Brauer's centralizer algebras ⋮ Cellular structure of \(q\)-Brauer algebras. ⋮ Brauer algebras and centralizer algebras for \(\text{SO}(2n,\mathbb{C})\) ⋮ On the radical of Brauer algebras. ⋮ Specht filtrations and tensor spaces for the Brauer algebra. ⋮ Tautological classes on the moduli space of hyperelliptic curves with rational tails ⋮ Set-partition tableaux and representations of diagram algebras ⋮ Discriminants of Brauer algebras. ⋮ A \(q\)-Brauer algebra ⋮ The Brauer algebra and the symplectic Schur algebra ⋮ Signed brauer's algebras ⋮ Unnamed Item ⋮ Dual partially harmonic tensors and Brauer-Schur-Weyl duality. ⋮ Signed brauer's algebras as centralizer algebras ⋮ The generalized Franchetta conjecture for some hyper-Kähler varieties. II ⋮ Structure of symplectic invariant Lie subalgebras of symplectic derivation Lie algebras ⋮ The Brauer category and invariant theory ⋮ On the semisimplicity of the Brauer centralizer algebras ⋮ A Brauer algebra theoretic proof of Littlewood's restriction rules ⋮ On endomorphisms of quantum tensor space ⋮ Differential Posets ⋮ The partition algebra revisited ⋮ The rook partition algebra

Cites Work

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• An algebra related to the orthogonal group
• The semisimplicity of \(\omega_f^n\)
• Zonal polynomials of the real positive definite symmetric matrices
• A Schensted-type correspondence for the symplectic group
• On the structure of Brauer's centralizer algebras
• The Distribution of the Latent Roots of the Covariance Matrix
• Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
• Homologie et cohomologie des algèbres de Lie
• On Symmetrized Kronecker Powers and the Structure of the Free Lie Ring

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