Matrix units for centralizer algebras

DOI10.1016/0021-8693(92)90109-YzbMath0761.16008MaRDI QIDQ1183308

Arun Ram, H. G. Wenzl

Publication date: 28 June 1992

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

zbMATH Keywords

Hecke algebrasgroup algebrassymmetric groupstensor productsirreducible representationsmatrix unitsBrauer's centralizer algebrasnatural representationsrepresentation of quantum groups

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Finite rings and finite-dimensional associative algebras (16P10) Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Semisimple Lie groups and their representations (22E46) Finite-dimensional division rings (16K20) Units, groups of units (associative rings and algebras) (16U60)

Related Items (19)

Quotients of representation rings ⋮ Strongly multiplicity free modules for Lie algebras and quantum groups ⋮ A Generalized Berele-Schensted Algorithm and Conjectured Young Tableaux for Intermediate Symplectic Groups ⋮ MATRIX UNITS FOR THE GROUP ALGEBRA kG_f = k((ℤ₂ × ℤ₂) ≀ S_f) ⋮ A quantum analogue of the first fundamental theorem of classical invariant theory ⋮ The fundamental invariant of the Hecke algebra Hn(q) characterizes the representations of Hn(q), S n, SUq(N), and SU(N) ⋮ On centralizer algebras for spin representations ⋮ Quantum groups and subfactors of type B, C, and D ⋮ A combinatorial description of the centralizer algebras connected to the Links-Gould invariant ⋮ Hecke algebras, 𝑈_{𝑞}𝑠𝑙_{𝑛}, and the Donald-Flanigan conjecture for 𝑆_{𝑛} ⋮ ON THE U_q(osp(1|2n)) AND U_-q(so(2n + 1)) UNCOLORED QUANTUM LINK INVARIANTS ⋮ Tilting modules, dominant dimensions and Brauer-Schur-Weyl duality ⋮ A \(q\)-Brauer algebra ⋮ Brauer algebra dual modules and polytabloids ⋮ Tresses et structure entière sur la catégorie des représentations de sl_Nquantique ⋮ Canonical idempotents of multiplicity-free families of algebras ⋮ On Brauer algebra simple modules over the complex field ⋮ \(q\)-centralizer algebras for spin groups ⋮ Braids and invariants of 3-manifolds

Cites Work

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• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum R matrix for the generalized Toda system
• A q-analogue of Young symmetrizer
• The Yang-Baxter equation and invariants of links
• On the structure of Brauer's centralizer algebras
• Hecke algebras of type \(A_ n\) and subfactors
• Quantum groups and subfactors of type B, C, and D
• Representations of \(AF\)-algebras and of the group \(U(\infty)\)
• Index for subfactors
• Differential Posets
• Dimensions of irreducible representations of the classical Lie groups
• Inductive Limits of Finite Dimensional C ∗ -Algebras
• On Quantitative Substitutional Analysis

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