Representation theory. A first course

Fulton, W., & Harris, J. (1991). Representation theory. A first course: A First Course. Springer-Verlag.

Type

Book

Intellectual base

Textbook

Year

1991

Volume

129

DOI

10.1007/978-1-4612-0979-9

ISBN

9783540005391

DOI registrant

Springer Nature

Link

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

Cited from

mathematics

Cited by

11 citations across 11 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.

    Supported in partVerified against the publisher's abstract

    Fulton & Harris is the standard introduction to group actions on vector spaces; the retrieved abstract frames group actions but never mentions a map coupling two group actions, so it supports the setting, not the intertwiner sentence.

    “Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces.”

    Read by an automated reader; not a human review. How support was checked

Domain-specific

• Frobenius–Schur indicator
  • For a compact or finite group, the indicator is an averaged character value, classically taking 1, 0, or −1 according to the existence and symmetry of invariant bilinear forms.
• 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.

Verification

Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.

Does it back the claim? Read against the text for 1 of 11 citations: 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.

Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.

See how references were verified.

Links previously used in the corpus

Before the registry existed this work was also linked 1 other way.

• https://doi.org/10.1007/978-1-4612-0979-9 ×3

Registry ID ref:5494cacde165 · see in the full table