On the jordan form of the tensor product over fields of prime characteristic

DOI10.1080/03081089508818371zbMath0830.15005OpenAlexW2034144360MaRDI QIDQ4853919

C. W. Norman

Publication date: 5 November 1995

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081089508818371

zbMATH Keywords

polynomialsJordan formtensor productJordan matriceselementary divisorscompanion matricesnilpotent transformationJordan basis

Mathematics Subject Classification ID

Multilinear algebra, tensor calculus (15A69) Canonical forms, reductions, classification (15A21)

Related Items (17)

Bases for fixed points of unipotent elements acting on the tensor square and the spaces of alternating and symmetric 2-tensors ⋮ On a Question of Glasby, Praeger, and Xia ⋮ `Norman involutions' and tensor products of unipotent Jordan blocks ⋮ On the Jordan form of a family of linear mappings ⋮ Decomposing modular tensor products: `Jordan partitions', their parts and \(p\)-parts ⋮ Exterior and symmetric powers of modules for cyclic 2-groups. ⋮ Adjoint Jordan blocks for simple algebraic groups of type \(C_{\ell}\) in characteristic two ⋮ On Jordan bases for the tensor product and Kronecker sum and their elementary divisors over fields of prime characteristic ⋮ Elementary divisors of tensor products and \(p\)-ranks of binomial matrices. ⋮ Generators for decompositions of tensor products of modules associated with standard Jordan partitions ⋮ Generators for decompositions of tensor products of modules. ⋮ Jordan blocks of nilpotent elements in some irreducible representations of classical groups in good characteristic ⋮ Decomposition of exterior and symmetric squares in characteristic two ⋮ Decomposing tensor products and exterior and symmetric squares ⋮ Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic ⋮ On the decomposition of the exterior square of an indecomposable module of a cyclic p-group ⋮ A NEW ALGORITHM FOR DECOMPOSING MODULAR TENSOR PRODUCTS

Cites Work

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• Combinatorial verification of the elementary divisors of tensor products
• On Jordan bases for two related linear mappings
• A canonical basis for the matrix transformation \(X \to AX+XB\)
• A canonical basis for the matrix transformation \(X\to AXB\)
• Elementary divisors of tensor products
• On direct product matrices
• The Normal Form of Compound and Induced Matrices
• Decomposition of Products of Modular Representations
• The Modular Representation Ring of a Cyclic p -Group
• On Induced and Compound Matrices

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