10.1007/978-1-4612-0979-9

Fulton, W., & Harris, J. (1991). 10.1007/978-1-4612-0979-9: A First Course. Representation Theory: A First Course.

Type

Book

Intellectual base

Textbook

Year

1991

DOI

10.1007/978-1-4612-0979-9

ISBN

9783540005391

Link

https://link.springer.com/book/10.1007/978-1-4612-0979-9

Cited from

mathematics

Cited by

10 citations across 10 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Equivariance
  • The defining feature is that two distinct group actions — one on the input space, one on the output space — are tied together by the map, so that the map "respects" the symmetry rather than destroying or merely tolerating it.

    This sourceStandard introduction to representations of finite groups and Lie groups/algebras.

Domain-specific

• Hermite reciprocity
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Induced representation
  • For topological or locally compact groups, function spaces, continuity, measures, and unitary structure replace the finite algebraic direct sum and must be specified.
• Outer automorphism group
  • Outer-group elements are cosets rather than canonical automorphisms, so an outer action need not lift to an actual action; completeness, center and exceptional symmetric-group cases require separate conditions.
• Quaternionic representation
  • … instance directly demonstrates that group, field, representation, antilinear operator, equivariance, J-squared convention, irreducibility, and indicator criterion are fixed consistently. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
• Subrepresentation
  • A subrepresentation is a subspace W of a representation V satisfying π(g)W⊆W for every acting element, equipped with the restricted action.
• Symmetrization
  • Antisymmetrization instead weights each permutation by its sign.
• Symplectic Representation
  • These are not decorative equations: they are the recognition test and the source of invariant duality, paired weights, determinant restrictions, and decomposition constraints.

    This sourceCanonical treatment of representations and classical symplectic groups/Lie algebras.

• Tensor representation
  • Tensor representation is a representation of a general linear or matrix group obtained from finite tensor products of a fundamental representation and its dual, including their irreducible factors.
• Trivial Representation
  • The multiplicity of the trivial irreducible therefore measures invariant vectors, invariant tensors, or symmetry singlets.

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